{"id":254,"date":"2023-07-10T11:04:37","date_gmt":"2023-07-10T11:04:37","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%b7%d8%a7%d8%a6%d8%b1%d8%a7%d8%aa-%d9%85%d8%aa%d9%88%d8%a7%d8%b2%d9%8a%d8%a9\/"},"modified":"2023-07-10T11:04:37","modified_gmt":"2023-07-10T11:04:37","slug":"%d8%b7%d8%a7%d8%a6%d8%b1%d8%a7%d8%aa-%d9%85%d8%aa%d9%88%d8%a7%d8%b2%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%b7%d8%a7%d8%a6%d8%b1%d8%a7%d8%aa-%d9%85%d8%aa%d9%88%d8%a7%d8%b2%d9%8a%d8%a9\/","title":{"rendered":"\u0637\u0627\u0626\u0631\u0627\u062a \u0645\u062a\u0648\u0627\u0632\u064a\u0629"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646: \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0623\u0645\u062b\u0644\u0629\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c&#8230; <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-planos-paralelos\"><\/span> \u0645\u0627 \u0647\u0645\u0627 \u0627\u0644\u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u062a\u0627\u0646\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 \u062f\u0627\u0626\u0645\u064b\u0627 \u0645\u062a\u0633\u0627\u0648\u064a\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0644\u0627 \u064a\u062a\u0642\u0627\u0637\u0639\u0627\u0646 \u0623\u0628\u062f\u064b\u0627 \u0648\u0644\u064a\u0633 \u0628\u064a\u0646\u0647\u0645\u0627 \u0623\u064a \u0634\u064a\u0621 \u0645\u0634\u062a\u0631\u0643.<\/strong> <\/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\/plans-paralleles-1.webp\" alt=\"\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629\" class=\"wp-image-2815\" width=\"332\" height=\"208\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0646 \u0648\u0636\u0639 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0644\u064a\u0633 \u0647\u0648 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0627\u0644\u0648\u062d\u064a\u062f \u0627\u0644\u0645\u0645\u0643\u0646 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a\u060c \u062d\u064a\u062b \u0623\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3) \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646\u0627 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 \u0623\u0648 \u0645\u062a\u0637\u0627\u0628\u0642\u064a\u0646 \u0623\u064a\u0636\u064b\u0627. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-planos-son-paralelos\"><\/span> \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0643 \u0645\u0639\u0631\u0641\u0629 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u0627\u0646\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0643 \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0623\u0645 \u0644\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u062f\u0621\u0627\u064b \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\u064a\u0629) \u0644\u062e\u0637\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\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-679de3a47957678b36c7ce59c2ac3415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ A_1x+B_1y+C_1z+D_1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" 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-2685d26d2a3ccd531ef0fb45769d013a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A_2x+B_2y+C_2z+D_2 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0645\u0639\u0627\u0645\u0644\u0627\u062a\u0647\u0645\u0627 A \u0648B \u0648C \u0645\u062a\u0646\u0627\u0633\u0628\u0629 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636 \u0648\u0644\u064a\u0633 \u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 D. \u0648\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u062d\u062f\u062b \u0627\u0644\u062a\u0648\u0627\u0632\u064a \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0639\u0646\u062f\u0645\u0627 \u062a\u062a\u062d\u0642\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\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-10e8a78403a97a98ff8efc375d963d0d_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 ]}]{equation*}      \\cfrac{A_1}{A_2}=\\cfrac{B_1}{B_2} = \\cfrac{C_1}{C_2}\\neq \\cfrac{D_1}{D_2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-dos-planos-paralelos\"><\/span> \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\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-83a8236303807a26eff03df9b5aae7ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x+2y-4z+1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" 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-99a5206f765bfb3f6441f5c41bba99dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+y-2z+5 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u062e\u0637\u0637\u0627\u062a \u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0644\u0623\u0646 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a X\u060c Y\u060c Z \u062a\u062a\u0646\u0627\u0633\u0628 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636\u060c \u0648\u0644\u0643\u0646 \u0644\u064a\u0633 \u0645\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0633\u062a\u0642\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-0dabd414a6a2dc053e2b91f27d89ab8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{3} =\\cfrac{2}{1} =\\cfrac{-4}{-2} \\neq \\cfrac{1}{5} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"261\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"calcular-la-distancia-entre-dos-planos-paralelos\"><\/span> \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646 \u064a\u0642\u0639\u0627\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0644\u0630\u0644\u0643 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u062e\u0630 \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0623\u062d\u062f \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0622\u062e\u0631.<\/strong> \u0644\u0630\u0644\u0643\u060c \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0645\u0639\u0631\u0641\u0629 <a href=\"https:\/\/mathority.org\/ar\">\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u0645\u0633\u062a\u0648\u0649<\/a> . <\/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\/distance-entre-deux-plans-paralleles.webp\" alt=\"\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646\" class=\"wp-image-2647\" width=\"401\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0646\u0647\u0627 \u0637\u0631\u064a\u0642\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0637\u0631\u064a\u0642\u0629 \u0623\u0628\u0633\u0637 \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643 \u0639\u0646\u062f\u0645\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\u064a\u0629) \u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\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-a277aae741d0cfe8200b7c338f57343f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D_1=0 \\qquad \\qquad  \\pi_2 : \\ Ax+By+Cz+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"528\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0635\u064a\u063a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646<\/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-fba7a69f403ec1b933994e987e1ff71b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}} \\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"343\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0641\u0645\u0646 \u0627\u0644\u0645\u0624\u0643\u062f \u0623\u0646\u0647 \u0645\u0646 \u0627\u0644\u0623\u0633\u0647\u0644 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0645\u062c\u0631\u062f \u0645\u0633\u0623\u0644\u0629 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0648\u0647\u0630\u0627 \u0643\u0644 \u0634\u064a\u0621\u060c \u0644\u0643\u0646 \u0630\u0644\u0643 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0634\u0643\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u0639\u062a\u0642\u062f \u0623\u0646\u0647 \u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0634\u0631\u062d \u0643\u0644\u062a\u0627 \u0627\u0644\u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u062a\u0641\u0636\u0644\u0647\u0627.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0648\u0641 \u0646\u062d\u0633\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\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-a9cd1abd1a84a5a230fb855c75c59e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 4x-2y-4z+7=0 \\qquad \\qquad  \\pi_2 : \\ 8x-4y-8z+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"471\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u064b\u0627 \u0623\u0646 \u0646\u062a\u062d\u0642\u0642 \u0645\u0646 \u0623\u0646\u0646\u0627 \u0646\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u062a\u064a\u0646. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u062c\u0645\u064a\u0639 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629 \u0645\u062a\u0646\u0627\u0633\u0628\u0629 \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629\u060c \u0644\u0630\u0627 \u0641\u0647\u0645\u0627 \u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646 \u0641\u0639\u0644\u064a\u064b\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-e13f3d3e18910312a6604d299010da6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{8}=\\cfrac{-2}{-4}=\\cfrac{-4}{-8}\\neq \\cfrac{7}{2} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0635\u0637\u0644\u062d\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u0644\u0643\u0646 \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062d\u0642\u064a\u0642 \u0630\u0644\u0643 \u0628\u0642\u0633\u0645\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0646\u064a \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \u0639\u0644\u0649 \u0627\u062b\u0646\u064a\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-d159a803fe606b074b2fbafbf792829d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ \\cfrac{8x-4y-8z+2}{2}=\\cfrac{0}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"204\" 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-0098cb52d72e1305e5cc6daee535dee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 4x-2y-4z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0623\u0635\u0628\u062d\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0622\u0646 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C. \u0644\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0633\u0647\u0648\u0644\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\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-3f78d3a0f1fd3a6c00acfd51c160dc8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"202\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0646\u062d\u0644 \u0627\u0644\u0639\u0645\u0644\u064a\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-ebaa9342424e4e1c6df12cac1f2658fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 1-7\\rvert}{\\sqrt{4^2+(-2)^2+(-4)^2}}= \\cfrac{\\lvert -6\\rvert}{\\sqrt{36}} = \\cfrac{6}{6} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"369\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0623\u062d\u062f \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0622\u062e\u0631 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0648\u062d\u062f\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-planos-paralelos\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u0627\u0646\u0639\u0643\u0627\u0633\u064a\u0629<\/strong> : \u0643\u0644 \u0645\u0633\u062a\u0648\u0649 \u0645\u0648\u0627\u0632\u064a \u0644\u0646\u0641\u0633\u0647.<\/li>\n<\/ul>\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-e0c49b095c95d593d607cda423172a99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\parallel \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062a\u0646\u0627\u0638\u0631<\/strong> : \u0625\u0630\u0627 \u0643\u0627\u0646 \u0623\u062d\u062f \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u0648\u0627\u0632\u064a\u0627 \u0644\u0644\u0622\u062e\u0631\u060c \u0641\u0625\u0646 \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u064a \u0645\u0648\u0627\u0632\u064a \u0644\u0644\u0623\u0648\u0644 \u0623\u064a\u0636\u0627. \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u062a\u0645\u062a\u0644\u0643\u0647\u0627 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629.<\/li>\n<\/ul>\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-6744d81df1ba01b40bf2dd2c429ead6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\parallel \\pi_2 \\ \\longrightarrow \\ \\pi_2 \\parallel \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u062e\u0627\u0635\u064a\u0629 \u0645\u062a\u0639\u062f\u064a\u0629<\/strong> : \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0648\u0627\u0632\u064a\u0627 \u0644\u0645\u0633\u062a\u0648\u0649 \u0622\u062e\u0631\u060c \u0648\u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0646\u064a \u0645\u0648\u0627\u0632\u064a \u0644\u0645\u0633\u062a\u0648\u0649 \u062b\u0627\u0644\u062b\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0623\u0648\u0644 \u0645\u0648\u0627\u0632\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b \u0623\u064a\u0636\u0627.<\/li>\n<\/ul>\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-cbdb26cf7c9104ca3111695826de0161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\pi_1 \\parallel \\pi_2\\\\[2ex] \\pi_2 \\parallel \\pi_3 \\end{array} \\right\\} \\longrightarrow \\ \\pi_1 \\parallel \\pi_3\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"176\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646: \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0623\u0645\u062b\u0644\u0629\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c&#8230; \u0645\u0627 \u0647\u0645\u0627 \u0627\u0644\u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u062a\u0627\u0646\u061f \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 \u062f\u0627\u0626\u0645\u064b\u0627 \u0645\u062a\u0633\u0627\u0648\u064a\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0644\u0627 \u064a\u062a\u0642\u0627\u0637\u0639\u0627\u0646 \u0623\u0628\u062f\u064b\u0627 \u0648\u0644\u064a\u0633 \u0628\u064a\u0646\u0647\u0645\u0627 \u0623\u064a \u0634\u064a\u0621 \u0645\u0634\u062a\u0631\u0643. \u0625\u0646 \u0648\u0636\u0639 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0644\u064a\u0633 \u0647\u0648 \u0627\u0644\u0645\u0648\u0636\u0639 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%b7%d8%a7%d8%a6%d8%b1%d8%a7%d8%aa-%d9%85%d8%aa%d9%88%d8%a7%d8%b2%d9%8a%d8%a9\/\"> <span class=\"screen-reader-text\">\u0637\u0627\u0626\u0631\u0627\u062a \u0645\u062a\u0648\u0627\u0632\u064a\u0629<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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