{"id":268,"date":"2023-07-10T04:25:24","date_gmt":"2023-07-10T04:25:24","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d8%b7%d8%a7%d8%a6%d8%b1%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1\/"},"modified":"2023-07-10T04:25:24","modified_gmt":"2023-07-10T04:25:24","slug":"%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d8%b7%d8%a7%d8%a6%d8%b1%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d8%b7%d8%a7%d8%a6%d8%b1%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1\/","title":{"rendered":"\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0637\u0627\u0626\u0631\u0629 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0627\u0644\u0635\u064a\u063a \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0627\u0644\u062e\u0637\u0629 \u0648\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627. \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0623\u064a\u0636\u064b\u0627 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u0645\u0639 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-ecuacion-del-plano\"><\/span> \u0645\u0627 \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0637\u0627\u0626\u0631\u0629\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c <strong>\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649<\/strong> \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0633\u0645\u062d \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u0631\u064a\u0627\u0636\u064a\u064b\u0627. \u0644\u0630\u0627\u060c \u0644\u0625\u064a\u062c\u0627\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0641\u0625\u0646\u0643 \u062a\u062d\u062a\u0627\u062c \u0641\u0642\u0637 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0648\u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u0633\u062a\u0642\u0644\u064a\u0646 \u062e\u0637\u064a\u064b\u0627 \u064a\u0646\u062a\u0645\u064a\u0627\u0646 \u0625\u0644\u0649 \u0630\u0644\u0643 \u0627\u0644\u0645\u0633\u062a\u0648\u0649.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0628\u0644 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u0641\u064a \u0634\u0631\u062d \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u062a\u0641\u0647\u0645 \u0645\u0627 \u0647\u0648 <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0647\u0646\u062f\u0633\u0629-\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629\/\">\u0627\u0644\u0645\u0633\u062a\u0648\u064a (\u0627\u0644\u0647\u0646\u062f\u0633\u0629)<\/a> \u060c \u0648\u0625\u0644\u0627 \u0633\u062a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0623\u0634\u064a\u0627\u0621 \u0644\u0646 \u062a\u0641\u0647\u0645\u0647\u0627. \u0625\u0630\u0627 \u0644\u0645 \u062a\u0643\u0646 \u0648\u0627\u0636\u062d\u064b\u0627 \u062a\u0645\u0627\u0645\u064b\u0627\u060c \u0641\u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0630\u0644\u0643 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0631\u0627\u0628\u0637\u060c \u062d\u064a\u062b \u0642\u0645\u0646\u0627 \u0628\u062a\u0631\u0643\u064a\u0632 \u0643\u0644 \u0645\u0627 \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0645\u0639\u0631\u0641\u062a\u0647 \u062d\u0648\u0644 \u0627\u0644\u062e\u0637\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-las-ecuaciones-del-plano\"><\/span> \u0645\u0627 \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u0629\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0641\u064a \u062a\u0639\u0631\u064a\u0641 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0645\u0633\u0637\u062d \u0643\u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0627\u062d\u062f\u0629 \u0648\u0645\u062a\u062c\u0647\u064a\u0646. <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equations-planes.webp\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0637\u0627\u0626\u0631\u0629 xy \u0639\u0644\u0649 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0634\u0631\u0637 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0644\u0643\u064a \u062a\u062a\u0648\u0627\u0641\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u0648 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0644\u0645\u062a\u062c\u0647\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u062e\u0637\u064a\u060c \u0623\u064a \u0623\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0644\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646\u0627 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0645\u0639 \u0628\u0639\u0636\u0647\u0645\u0627 \u0627\u0644\u0628\u0639\u0636.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u062c\u0645\u064a\u0639 \u0623\u0646\u0648\u0627\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a: <strong>\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0629<\/strong> \u060c <strong>\u0648\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629<\/strong> \u060c <strong>\u0648\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629)<\/strong> \u060c <strong>\u0648\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0627\u0646\u0648\u0646\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629)<\/strong> \u0644\u0644\u0645\u0633\u062a\u0648\u0649.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062b\u0645 \u0633\u0646\u0631\u0649 \u0628\u0627\u0644\u062a\u0641\u0635\u064a\u0644 \u0634\u0631\u062d \u0648\u0635\u064a\u063a\u0629 \u062c\u0645\u064a\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u0629. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ecuacion-vectorial-del-plano\"><\/span> \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0644\u0644\u0637\u0627\u0626\u0631\u0629<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u0645\u062a\u062c\u0647\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649<\/strong> \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9227901692832cb0c176a896d35e896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      (x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644\u0647\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78b41d21b63c22ec05d3f93576a897e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+\\lambda (\\text{u}_x,\\text{u}_y,\\text{u}_z) + \\mu (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"398\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0647\u0645\u0627 \u0639\u062f\u062f\u0627\u0646 \u0642\u064a\u0627\u0633\u064a\u0627\u0646\u060c \u0623\u064a \u0639\u062f\u062f\u0627\u0646 \u062d\u0642\u064a\u0642\u064a\u0627\u0646. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ecuaciones-parametricas-del-plano\"><\/span> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0629<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0645\u062a\u062c\u0647\u0629. \u0623\u062f\u0646\u0627\u0647 \u064a\u0645\u0643\u0646\u0643 \u0631\u0624\u064a\u0629 \u0627\u0644\u0639\u0631\u0636 \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0629 \u0644\u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u062a\u0643\u0648\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78b41d21b63c22ec05d3f93576a897e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+\\lambda (\\text{u}_x,\\text{u}_y,\\text{u}_z) + \\mu (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"398\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0639\u0645\u0644 \u0648\u0646\u0646\u0641\u0630 \u0623\u0648\u0644\u0627\u064b \u0645\u0646\u062a\u062c\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eb7c00ddf8ba235e3698c85a0f23db0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+ (\\lambda\\text{u}_x,\\lambda\\text{u}_y,\\lambda\\text{u}_z) +(\\mu\\text{v}_x,\\mu\\text{v}_y,\\mu\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"440\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0639\u062f\u064a\u0646 \u0646\u0636\u064a\u0641 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3ff52d13a3d4400800b0f72148f99c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x+\\lambda \\text{u}_x + \\mu \\text{v}_x,P_y+\\lambda \\text{u}_y + \\mu \\text{v}_y,P_z+\\lambda \\text{u}_z + \\mu \\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"467\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u062e\u0637\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u064a\u0639\u0627\u0628 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\u0643\u0644 \u0645\u062a\u063a\u064a\u0631 \u0639\u0644\u0649 \u062d\u062f\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e1791802331aa9973126b3d7c7f1b716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0647\u0645\u0627 \u0639\u062f\u062f\u0627\u0646 \u0642\u064a\u0627\u0633\u064a\u0627\u0646\u060c \u0623\u064a \u0639\u062f\u062f\u0627\u0646 \u062d\u0642\u064a\u0642\u064a\u0627\u0646.<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b77e9af6839a6bc60da39dd1798dd6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_x,\\text{u}_y,\\text{u}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u0647\u064a \u0645\u0643\u0648\u0646\u0627\u062a \u0623\u062d\u062f \u0627\u0644\u0645\u0648\u062c\u0647\u064a\u0646 \u0627\u0644\u0645\u0648\u062c\u0647\u064a\u0646 \u0644\u0644\u062e\u0637\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8a3eef2109d6a80a337c88337a1443e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -6px;\"><\/p>\n<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f61b32275ccdbca7f8d5e0b3c750dd35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_x,\\text{v}_y,\\text{v}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u0647\u064a \u0645\u0643\u0648\u0646\u0627\u062a \u0646\u0627\u0642\u0644 \u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0627\u0644\u0622\u062e\u0631 \u0644\u0644\u062e\u0637\u0629 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75c6a57a037206319f16dec389993ded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -6px;\"><\/p>\n<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ecuacion-implicita-o-general-del-plano\"><\/span> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0629<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u0645\u062a\u062c\u0647\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0623\u0648 \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0644 \u0627\u0644\u0645\u062d\u062f\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0648\u062c\u0639\u0644 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u062a\u0633\u0627\u0648\u064a 0:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68d67612dfa54d76666aa37b702a472f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}\\text{u}_x &amp; \\text{v}_x &amp; x-P_x \\\\[1.1ex]\\text{u}_y &amp; \\text{v}_y &amp; y-P_y \\\\[1.1ex]\\text{u}_z &amp; \\text{v}_z &amp; z-P_z \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0630\u0644\u0643 \u062a\u0643\u0648\u0646 <strong>\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u062e\u0637\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629<\/strong> \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7dcacf16123986ecd33dace4f4411914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle Ax+By+Cz+D=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u064a\u0633\u0645\u0649 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629 \u0623\u064a\u0636\u064b\u0627 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u064a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-o-segmentaria-del-plano\"><\/span> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0643\u0646\u0633\u064a \u0623\u0648 \u0627\u0644\u0642\u0637\u0639\u064a \u0644\u0644\u0637\u0627\u0626\u0631\u0629<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0623\u0648 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649<\/strong> \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c19853d465a703aa398bde04fa3222c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\cfrac{x}{a}+\\cfrac{y}{b} + \\cfrac{z}{c} = 1  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0647\u064a \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u0645\u062d\u0648\u0631 X.<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0647\u064a \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u0645\u062d\u0648\u0631 Y.<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0647\u0630\u0627 \u0647\u0648 \u0627\u0644\u0645\u0643\u0627\u0646 \u0627\u0644\u0630\u064a \u064a\u062a\u0642\u0627\u0637\u0639 \u0641\u064a\u0647 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0639 \u0627\u0644\u0645\u062d\u0648\u0631 Z. <\/li>\n<\/ul>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629) \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u0645\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27e298e3103f917bd81b20315b6d9025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"183\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u064b \u0646\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 D \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e6829185741f883a29bf004cbf570a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz=-D\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"166\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062b\u0645 \u0646\u0642\u0633\u0645 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \u0639\u0644\u0649 \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 D \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04843e22b4176c0ce921483f93dffeab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax+By+Cz}{-D}=\\cfrac{-D}{-D}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"176\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-278ce62f85ca44612254f48e96154726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax}{-D}+\\cfrac{By}{-D}+\\cfrac{Cz}{-D}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"166\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0643\u0633\u0648\u0631 \u0646\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a58254e773c7c14b5b337a4330997125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{-\\frac{D}{A}}+\\cfrac{y}{-\\frac{D}{A}}+\\cfrac{z}{-\\frac{D}{A}}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"167\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u0646\u0633\u062a\u0646\u062a\u062c \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u064a \u062a\u0633\u0645\u062d \u0628\u062d\u0633\u0627\u0628 \u0634\u0631\u0648\u0637 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0623\u0648 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86975df14352b1b0c2ca05d2daaf40f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=-\\cfrac{D}{A} \\qquad b=-\\cfrac{D}{B} \\qquad c=-\\cfrac{D}{C}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"260\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0644\u0643\u064a \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u062a\u0643\u0648\u064a\u0646 \u0647\u0630\u0627 \u0627\u0644\u0628\u062f\u064a\u0644 \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u0629\u060c \u064a\u062c\u0628 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0645\u062e\u062a\u0644\u0641\u0629 \u0639\u0646 \u0627\u0644\u0635\u0641\u0631\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u062c\u0646\u0628 \u0639\u062f\u0645 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0643\u0633\u0648\u0631. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"como-calcular-la-ecuacion-de-un-plano-a-partir-de-su-vector-normal\"><\/span> \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u062d\u062f\u0649 \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u0646\u0645\u0648\u0630\u062c\u064a\u0629 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0630\u064a \u062a\u0628\u062f\u0648 \u0639\u0644\u064a\u0647 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0633\u062a\u0648\u0649 \u0645\u0639\u064a\u0646 \u0628\u0645\u0639\u0644\u0648\u0645\u064a\u0629 \u0646\u0642\u0637\u0629 \u0648\u0645\u062a\u062c\u0647\u0647\u0627 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0623\u0648 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f). \u0644\u0630\u0644\u0643\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641 \u064a\u0639\u0645\u0644.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646 \u064a\u062c\u0628 \u0623\u0646 \u062a\u0639\u0644\u0645 \u0623\u0648\u0644\u0627\u064b \u0623\u0646 <strong>\u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a X \u0648Y \u0648Z \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u062a\u0637\u0627\u0628\u0642 <strong>\u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a<\/strong><\/strong> <strong>\u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629) \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0645\u0630\u0643\u0648\u0631.<\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27f3ee5d7e81864550f3b86fdd53e89d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\color{orange} \\boxed{ \\color{black} \\quad \\pi : \\ Ax+By+C+D = 0 \\quad \\iff \\quad \\vv{n} = (A,B,C) \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"540\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10affe1faee06a5faa4ef6d9c0473b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0623\u0646 \u0639\u0631\u0641\u0646\u0627 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0645\u062b\u0627\u0644\u0627\u064b \u0644\u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6df0e548515bb2b24f352853a2614015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648\u0623\u062d\u062f \u0646\u0627\u0642\u0644\u0627\u062a\u0647 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0647\u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44298f830c420011a4326017f5fd7cfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(3,-1,2) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0623\u0648 \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27e298e3103f917bd81b20315b6d9025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"183\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0647\u0643\u0630\u0627\u060c \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0627\u062f\u064a \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0623\u0646\u0647\u0627 \u062a\u0639\u0627\u062f\u0644 \u0645\u0643\u0648\u0646\u0627\u062a \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-596b3fdc65160234c06b0d28aebea74f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(3,-1,2) \\ \\longrightarrow \\ 3x-1y+2z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"322\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u064a\u0646\u0645\u0627 \u0646\u062d\u062a\u0627\u062c \u0641\u0642\u0637 \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0644\u0645\u0629 D. \u0648\u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u0639\u0648\u0636 \u0628\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6df0e548515bb2b24f352853a2614015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09a0b099394ba4634fb6d7aad3a627e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot 1-0+2\\cdot (-2)+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b90d57a1708925626a300c7e5db673ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3-4+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2dfb99a77bfcee1b72540db9cf579a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"91\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16ace3f6683252e5630a1091bbc0404e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u062e\u0637\u0629 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cde6db2f935eb7d0ad39141f86aab013_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{3x-y+2z+1 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"153\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-del-plano\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-967feca863a9a4d3f1e7f0267f5e75e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(0,-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648\u064a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u062a\u064a\u0646:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b080bdb2f119700090341574b7bbf489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ad5d13132fc818eac77b60b1ac15e13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(2,-1,5).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0645\u0639\u0631\u0641\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0648\u0645\u062a\u062c\u0647\u064a\u0646\u060c \u0648\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u062f\u064a\u0646\u0627 \u0645\u062a\u062c\u0647 \u0648\u0627\u062d\u062f \u0641\u0642\u0637\u060c \u0644\u0630\u0627 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0645\u062a\u062c\u0647 \u0622\u062e\u0631 \u0645\u0648\u062c\u0647 \u0644\u0644\u0645\u0633\u062a\u0648\u0649. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u064a\u062d\u062f\u062f \u0646\u0642\u0637\u062a\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b85ba6303c469618bd0d69f560c11535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-1,5) - (1,3,-1) = (1,-4,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0639\u0631\u0641\u0646\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0645\u062a\u062c\u0647\u064a \u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0646\u0642\u0637\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0644\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d80b8a9d79088c24cb1940b2abeb18bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0639\u0648\u0636 \u0628\u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0648\u0625\u062d\u062f\u0649 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-941c8d43b51f4c2f838a0ef55b1f87fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x,y,z)=(1,3,-1)+\\lambda (0,-2,3) + \\mu (1,-4,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062b\u0644\u0627\u062b \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df564519d92ccbe87c5500460231d2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,1,0) \\qquad B(2,-3,-1) \\qquad C(1,5,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0639\u0644\u064a\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u0633\u062a\u0642\u0644\u064a\u0646 \u062e\u0637\u064a\u064b\u0627 \u064a\u0631\u062a\u0628\u0637\u0627\u0646 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0648\u0644\u0647\u0630\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u062d\u062f\u062f\u064a\u0646 \u0628\u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062b\u0644\u0627\u062b: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14d7f4f29cbdc14a69357bf1b8f29b4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-3,-1) - (4,1,0) = (-2,-4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a33c0974226c3e3c0a51de22c0b8b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (1,5,3) - (4,1,0) = (-3,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u064a\u0646 \u063a\u064a\u0631 \u0645\u062a\u0646\u0627\u0633\u0628\u0629\u060c \u0644\u0630\u0627 \u0641\u0647\u0645\u0627 \u0645\u0633\u062a\u0642\u0644\u0627\u0646 \u062e\u0637\u064a\u064b\u0627 \u0639\u0646 \u0628\u0639\u0636\u0647\u0645\u0627 \u0627\u0644\u0628\u0639\u0636.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0639\u0631\u0641\u0646\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0645\u062a\u062c\u0647\u064a \u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0639\u0648\u0636 \u0628\u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0648\u0625\u062d\u062f\u0649 \u0646\u0642\u0627\u0637 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0644\u0627\u062b \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f57edaf8a85108cffb796470ffca8484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=4 + \\lambda \\cdot (-2)+ \\mu \\cdot (-3) \\\\[1.7ex] y=1 + \\lambda \\cdot (-4) + \\mu \\cdot 4 \\\\[1.7ex] z=0 + \\lambda\\cdot (-1) + \\mu \\cdot 3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"218\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cab5ddc074bd7df6849d71854207cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=4 -2 \\lambda-3\\mu } \\\\[1.7ex] \\bm{y=1-4 \\lambda+4 \\mu } \\\\[1.7ex] \\bm{z=-\\lambda + 3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b61f338575699a918d594595ddc6fb02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648\u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5150cc543174c7c079a38b016685eb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(4,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0664398c6f1938e4ec5efaae48ab1c70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(5,3,-1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0623\u0648 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u062d\u0644 \u0627\u0644\u0645\u062d\u062f\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0627\u0644\u0645\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0648\u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0648\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0646\u0642\u0637\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-917f1770ff2a17897e5df76998ec3519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}\\text{u}_x &amp; \\text{v}_x &amp; x-P_x \\\\[1.1ex]\\text{u}_y &amp; \\text{v}_y &amp; y-P_y \\\\[1.1ex]\\text{u}_z &amp; \\text{v}_z &amp; z-P_z \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0646\u0639\u0648\u0636 \u0628\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0648\u0627\u0644\u0646\u0642\u0637\u0629 \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02e103601cd9992a8a8c087d016a08c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}4 &amp; 5 &amp; x+2 \\\\[1.1ex]1 &amp; 3 &amp; y-1 \\\\[1.1ex]3&amp; 1 &amp; z+1 \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 3\u00d73 \u0628\u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u062a\u062e\u062a\u0627\u0631\u0647\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ec35e71b9cca25aa9907c97da2ea2e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12(z+1)+15(y-1)+1(x+2)-9(x+2)-4(y-1)-5(z+1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u062a\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fea5513ce57c88cac89a695b47b7a0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8(x+2)+11(y-1)+7(z+1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b965060b2baad7f1b7fa66e0555a23f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x-16+11y-11+7z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"262\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52635b24c2d396ff9a47fbd210c56bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x+11y+7z-20= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u062e\u0637\u0629 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc97887dad7e25ff823eee155fb58358_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-8x+11y+7z-20 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0637\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10de27107c1cf63dc889433e271d4a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u064a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0627\u0644\u062e\u0637\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54a545de55c14f27d77bfda0188789a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi : \\ 2x+y+6z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"184\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0643\u064a \u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u064a\u062c\u0628 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u062a\u0647\u0627. \u0644\u0630\u0644\u0643\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25ef56f6218537e6592c6ce17e0c3cb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+y+6z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"153\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10de27107c1cf63dc889433e271d4a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b30e787cb2dfac5e87b0758b866e10a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (-1)+5+6\\cdot (-3)-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66acebc4d56a2fb70fe23b2ead99dcc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2+5-18-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"155\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64706704bc6f3ef930293722159a8861_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-20\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"63\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0646\u0642\u0637\u0629 \u0644\u0627 \u062a\u062d\u062a\u0631\u0645 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c <strong>\u0644\u0630\u0627 \u0641\u0647\u064a \u0644\u064a\u0633\u062a \u062c\u0632\u0621\u064b\u0627 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649.<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u062a\u0643\u0648\u0646 \u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\u064a\u0629) \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3bae7c36a177b1d78c043d5cb96e89a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-2y-6z+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"162\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627 \u0646\u062d\u0630\u0641 \u0627\u0644\u062d\u062f \u0627\u0644\u0645\u0633\u062a\u0642\u0644 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82645f1698125207e2f86dc92d0d19d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-2y-6z=-6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"145\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062b\u0645 \u0646\u0642\u0633\u0645 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \u0639\u0644\u0649 \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 D \u0639\u0644\u0627\u0645\u0629 \u0627\u0644\u062a\u063a\u064a\u064a\u0631: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0e67dcc4d588043160bee40c086a1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x-2y-6z}{-6}=\\cfrac{-6}{-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"155\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8dcb648b6776e874b07b18a16175d7a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3x}{-6}+\\cfrac{-2y}{-6}+\\cfrac{-6z}{-6}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0643\u0633\u0648\u0631 \u0646\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd67201799ce9fe131bb81beb6050b3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{\\frac{-6}{3}}+\\cfrac{y}{\\frac{-6}{-2}}+\\cfrac{z}{\\frac{-6}{-6}}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"143\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0641\u0625\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0627\u0639\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629) \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-130fe442b594fbe32ced55d35b52fb9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\bm{x}}{\\bm{-2}}+\\cfrac{\\bm{y}}{\\bm{3}}+\\cfrac{\\bm{z}}{\\bm{1}}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"120\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 6<\/h3>\n<div class=\"wp-block-group\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-group__inner-container is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u0646\u0642\u0637\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e42bc8fa114f50a19858a526eabb6e30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648\u0623\u062d\u062f \u0646\u0627\u0642\u0644\u0627\u062a\u0647 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0647\u0648 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b007924d3ec5c7cd5de5d1d46cc86711_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(5,-2,-3) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0623\u0648 \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27e298e3103f917bd81b20315b6d9025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"183\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0646\u064b\u0627\u060c \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0627\u062f\u064a \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C\u060c \u0644\u0623\u0646\u0647\u0627 \u062a\u0633\u0627\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0627\u062f\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f4b71cc8d8c1610a5d5706ac44d1ad3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(5,-2,-3) \\ \\longrightarrow \\ 5x-2y-3z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u0646\u062d\u062a\u0627\u062c \u0641\u0642\u0637 \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0644\u0645\u0629 D. \u0648\u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u0639\u0648\u0636 \u0628\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e42bc8fa114f50a19858a526eabb6e30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-720c689bc073e6c0f865bf406d92cbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5\\cdot 3-2\\cdot 4-3\\cdot (-3)+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3edf41b26a3b9c8bdead74d05767ec60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15-8+9+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"147\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0db457697a3637eb92bff90460d8e98f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"16+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a2efb3d90e15e4474268d6de0570da4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=-16\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0641\u064a \u0627\u0644\u062e\u062a\u0627\u0645 \u0641\u0625\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u062e\u0637\u0629 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee0c114a24764dd24df9d58aab7155ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{5x-2y-3z-16 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 7<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u062e\u0637<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648\u064a\u0643\u0648\u0646 \u0645\u0648\u0627\u0632\u064a\u0627 \u0644\u0644\u064a\u0645\u064a\u0646<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0643\u0648\u0646\u0647\u0627 \u0627\u0644\u062e\u0637\u0648\u0637: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624f315685b292c4bb05e9cb4b931a97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=1+t \\\\[1.7ex] y=2-3t\\\\[1.7ex] z=4+2t \\end{cases} \\qquad \\qquad s: \\ \\frac{x-4}{2} = \\frac{y+3}{2}= \\frac{z-2}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"424\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0639\u0644\u064a\u0646\u0627 \u0645\u0639\u0631\u0641\u0629 \u0645\u062a\u062c\u0647\u064a \u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u064a\u062e\u0628\u0631\u0646\u0627 \u0627\u0644\u0625\u0639\u0644\u0627\u0646 \u0623\u0646\u0647 \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0633\u0637\u0631<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648\u0645\u0646 \u062b\u0645\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0623\u062e\u0630 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u062e\u0637 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u062a\u062e\u0628\u0631\u0646\u0627 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u0623\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0648\u0627\u0632\u064a \u0644\u0644\u062e\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cc36ef269909ae645021a09d5e91016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0644\u0630\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0647\u0630\u0627 \u0627\u0644\u062e\u0637 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062d\u0642<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647\u0627 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0643\u0648\u0646\u0627\u062a \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647\u0647\u0627 \u0647\u064a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0639\u0644\u0645\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b40bdea86f773b36fb40078fb4ddf23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(1,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u062e\u0637 \u0647\u064a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d565383a925076ae118032f7b9b62f7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u062e\u0637 \u0645\u0633\u062a\u0642\u064a\u0645<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u062a\u0643\u0648\u0646 \u0639\u0644\u0649 \u0635\u0648\u0631\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u062a\u0635\u0644\u0629\u060c \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0645\u0643\u0648\u0646\u0627\u062a \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647\u0647\u0627 \u0647\u064a \u0645\u0642\u0627\u0645\u0627\u062a \u0627\u0644\u0643\u0633\u0648\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8f571b217df7a6bbe833d706091457a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} =(2,2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u062e\u0637\u0629 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c81f4d8e5aa907f111b3389d5137736e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=1 + \\lambda \\cdot 1+ \\mu \\cdot 2 \\\\[1.7ex] y=2 + \\lambda \\cdot (-3) + \\mu \\cdot 2 \\\\[1.7ex] z=4 + \\lambda\\cdot 2 + \\mu \\cdot (-3) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"189\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fccd86ac9a3e4084e324d8e5b1071e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=1 + \\lambda+2\\mu } \\\\[1.7ex] \\bm{y=2-3 \\lambda+2 \\mu } \\\\[1.7ex] \\bm{z=4+2\\lambda -3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0627\u0644\u0635\u064a\u063a \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0627\u0644\u062e\u0637\u0629 \u0648\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627. \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0623\u064a\u0636\u064b\u0627 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u0645\u0639 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u0629. \u0645\u0627 \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0637\u0627\u0626\u0631\u0629\u061f \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0633\u0645\u062d \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u0631\u064a\u0627\u0636\u064a\u064b\u0627. \u0644\u0630\u0627\u060c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d8%b7%d8%a7%d8%a6%d8%b1%d8%a9-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1\/\"> <span class=\"screen-reader-text\">\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0637\u0627\u0626\u0631\u0629 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[15],"tags":[],"class_list":["post-268","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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