{"id":274,"date":"2023-07-10T01:20:15","date_gmt":"2023-07-10T01:20:15","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%b9%d9%84%d9%89-%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%a7%d9%84%d8%ae%d8%b7-%d9%88%d8%a7%d9%84%d9%85%d8%b3%d8%aa\/"},"modified":"2023-07-10T01:20:15","modified_gmt":"2023-07-10T01:20:15","slug":"%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%b9%d9%84%d9%89-%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%a7%d9%84%d8%ae%d8%b7-%d9%88%d8%a7%d9%84%d9%85%d8%b3%d8%aa","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%b9%d9%84%d9%89-%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%a7%d9%84%d8%ae%d8%b7-%d9%88%d8%a7%d9%84%d9%85%d8%b3%d8%aa\/","title":{"rendered":"\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0633\u062a\u062a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u062d\u0648\u0644 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-el-angulo-entre-una-recta-y-un-plano\"><\/span> \u0645\u0627 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0637\u0627\u0626\u0631\u0629\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0625\u0633\u0642\u0627\u0637\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649. <\/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\/angle-entre-une-ligne-et-un-plan.webp\" alt=\"\u0645\u0627 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0637\u0627\u0626\u0631\u0629\u061f\" class=\"wp-image-3943\" width=\"500\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u062a\u0643\u0645\u0644\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0630\u0643\u0648\u0631 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649. \u0644\u0630\u0644\u0643\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-una-recta-y-un-plano\"><\/span> \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u062e\u0637\u060c \u0639\u0644\u064a\u0643 \u0623\u0646 \u062a\u0639\u0631\u0641 \u0643\u064a\u0641\u064a\u0629 <a href=\"https:\/\/mathority.org\/ar\/\u0643\u064a\u0641\u064a\u0629-\u062d\u0633\u0627\u0628-\u0627\u0644\u0632\u0627\u0648\u064a\u0629-\u0628\u064a\u0646-\u0645\u062a\u062c\u0647\u064a\u0646-\u0627\u0654\u0645\u062b\u0644\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646<\/a> . \u0633\u062a\u062c\u062f \u0641\u064a \u0627\u0644\u0635\u0641\u062d\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0627\u0644\u0634\u0631\u062d \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629\u060c \u0644\u0630\u0627 \u0625\u0630\u0627 \u0643\u0646\u062a \u0644\u0627 \u062a\u062a\u0630\u0643\u0631 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0641\u0646\u0648\u0635\u064a\u0643 \u0628\u0625\u0644\u0642\u0627\u0621 \u0646\u0638\u0631\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0643\u0645\u0644\u0629 \u0644\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0648\u0627\u0642\u0639\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0627\u0644\u0645\u0630\u0643\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-e01bc8353ce87c4e409251c9a78dae8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}_r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"29\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648\u0627\u0644\u0646\u0627\u0642\u0644 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0637\u0627\u0626\u0631\u0629 \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45cf5bc44c73892962f2e851f74daacc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{n})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u060c \u0645\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u0639\u0627\u062f\u0644 \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-432b11c5cc73074467112392e29b46ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)=\\cos(90-\\alpha) =\\cfrac{\\lvert \\vv{\\text{v}}_r \\cdot \\vv{n} \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"247\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a<\/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\/angle-entre-une-droite-et-un-plan-formule.webp\" alt=\"\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0635\u064a\u063a\u0629\" class=\"wp-image-3975\" width=\"282\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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-50f32076ae1ee85f5b7c5a6d43a03089_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0644\u0644\u062e\u0637.<\/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-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\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0637\u0627\u0626\u0631\u0629. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-angulo-entre-una-recta-y-un-plano\"><\/span> \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0643\u064a \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0645\u0639\u0631\u0641\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644\u060c \u0625\u0644\u064a\u0643 \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u062e\u0637\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> \u0645\u0639 \u0627\u0644\u0637\u0627\u0626\u0631\u0629<\/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> \u0641\u0644\u062a\u0643\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647\u0645:<\/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-cb8b61cb99a7af826a63ee098efc3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x= 3-t \\\\[1.7ex] y = 2+4t \\\\[1.7ex] z=-3t \\end{cases}\\qquad\\qquad \\pi : \\ x-y+4z+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"392\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u062e\u0637 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629\u060c \u0628\u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647\u0647 \u0647\u0648:<\/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-f5c132cae76c4e7d2eef34b80dda60e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-1,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0636\u0645\u0646\u064a\u0629 (\u0623\u0648 \u0639\u0627\u0645\u0629)\u060c \u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0647\u0648:<\/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-6c8001623f05fee4f3266c426e184482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (1,-1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \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-60faf9957c871b9c9e62fe4ffc9b6973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-1,4,-3) \\cdot (1,-1,4)\\rvert}{\\sqrt{(-1)^2+4^2+(-3)^2} \\cdot \\sqrt{1^2+(-1)^2+4^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"393\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0642\u0648\u0645 \u0628\u0627\u0644\u062d\u0633\u0627\u0628\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-ecf6e128745b2cea94a0651a086d9708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -1\\cdot 1 +4 \\cdot (-1) + (-3) \\cdot 4\\rvert}{\\sqrt{26}\\cdot \\sqrt{18}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"289\" style=\"vertical-align: -16px;\"><\/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-d9ddce2ff5d93699f7583e541c33126d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-17|}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"125\" style=\"vertical-align: -16px;\"><\/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-df350eb37802b9a0fd712299478ece35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{17}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"117\" style=\"vertical-align: -16px;\"><\/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-77b7a2aaf4989013b48a34274af4b246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,79\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0643\u0633 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0648\u0646\u0648\u062c\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u0632\u0627\u0648\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-4222f5a3e1dc32c123215c725dffadcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,79) = \\bm{51,80\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u0628\u0644\u063a 51.80 \u062f\u0631\u062c\u0629 \u062a\u0642\u0631\u064a\u0628\u064b\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0623\u0646 \u0646\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0623\u0646\u0646\u0627 \u0625\u0630\u0627 \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 0\u00b0\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646 \u0623\u0648 \u0623\u0646 \u0627\u0644\u062e\u0637 \u0645\u0648\u062c\u0648\u062f \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u062a\u0633\u0627\u0648\u064a 90 \u062f\u0631\u062c\u0629\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u062a\u0639\u0627\u0645\u062f\u0627\u0646. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-angulo-entre-una-recta-y-un-plano\"><\/span>\u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649<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\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \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> \u0645\u0639 \u0627\u0644\u0637\u0627\u0626\u0631\u0629<\/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> \u0641\u0644\u062a\u0643\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647\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-187a958fc02bef31b18b2c2f95379015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\cfrac{x-1}{2} = \\cfrac{y+1}{-1} = \\cfrac{z+3}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" 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-97968f3ad3bc2327d83f308575a4607d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 3x+y+2z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" 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\"> \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u062e\u0637 \u0643\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647\u0647 \u0647\u0648:<\/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-ce8d892f9706e946ee38bea5601f420c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (2,-1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0639\u0644\u0649 \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0636\u0645\u0646\u064a\u0629 (\u0623\u0648 \u0639\u0627\u0645\u0629)\u060c \u0644\u0630\u0627 \u0641\u0625\u0646 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0647\u0648:<\/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-d9b2fb6c5a45dd5cff0e5c949ab7ee22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-f79b0514974ecd648d402afe09fce215_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(2,-1,-3) \\cdot (3,1,2)\\rvert}{\\sqrt{2^2+(-1)^2+(-3)^2} \\cdot \\sqrt{3^2+1^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"362\" style=\"vertical-align: -20px;\"><\/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-43b3452fc0559594f81d5793eb69bd50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert 2\\cdot 3 +(-1) \\cdot 1 + (-3) \\cdot 2\\rvert}{\\sqrt{14}\\cdot \\sqrt{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"275\" style=\"vertical-align: -16px;\"><\/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-0fae771d5c74fc70f8c235e7d977b97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-1|}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"116\" 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-4af96594105dfe56eb0b48a782596cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{1}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" 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-c26a8cbca5ca49005ddf750822a16359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,07\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0643\u0633 \u0627\u0644\u062c\u064a\u0628 \u0648\u0646\u0648\u062c\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u0632\u0627\u0648\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-6280b70e3e9db10239c8ed41338921b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,07) = \\bm{4,10\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/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\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a 4.10 \u062f\u0631\u062c\u0629.<\/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\"> \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \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> \u0645\u0639 \u0627\u0644\u0637\u0627\u0626\u0631\u0629<\/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> \u0641\u0644\u062a\u0643\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647\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-6a8165b8e50fbc7764c77d1a984de353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} 3x-y+4z+1=0 \\\\[2ex] x+2y-2z+6=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"198\" 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-4ef4dec995f97607a7e037e37eeb0b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ -4x+2y-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"167\" 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\"> \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u062e\u0637 \u0628\u0645\u0639\u0627\u062f\u0644\u0627\u062a\u0647 \u0627\u0644\u0636\u0645\u0646\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0639\u0627\u0645\u0629)\u060c \u0644\u0630\u0644\u0643 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u062c\u0647 \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0627\u0644\u0644\u062a\u064a\u0646 \u062a\u062d\u062f\u062f\u0627\u0646 \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-54cc86087728e7e163034c95afc55286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -1 &amp; 4 \\\\[1.1ex] 1 &amp;2&amp;-2 \\end{vmatrix}  = -6\\vv{i}+10\\vv{j}+7\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"236\" 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-d96017e2fa07a08307c10dc57ee61c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-6,10,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" 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 \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u0648:<\/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-029b4c2fd253e26ab1b4c273507b5527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (-4,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-dc066db1739212edabe5d565f906830b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-6,10,7) \\cdot (-4,2,0)\\rvert}{\\sqrt{(-6)^2+10^2+7^2} \\cdot \\sqrt{(-4)^2+2^2+0^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"374\" style=\"vertical-align: -20px;\"><\/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-d143bdbebf8285d4543063a31d886c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -6\\cdot (-4) +10 \\cdot 2 + 7 \\cdot 0\\rvert}{\\sqrt{185}\\cdot \\sqrt{20}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"271\" style=\"vertical-align: -16px;\"><\/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-35ceee51406f9d5bcc316b74690eb299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{44}{\\sqrt{3700}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"126\" style=\"vertical-align: -16px;\"><\/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-84549d70edc1d856e90c75ec50421389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,72\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0643\u0633 \u0627\u0644\u062c\u064a\u0628 \u0648\u0646\u0648\u062c\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u0632\u0627\u0648\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-e843d4cbca4933f7ba383adcd6566028_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,72) = \\bm{46,33\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/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\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a 46.33 \u062f\u0631\u062c\u0629.<\/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\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0642\u064a\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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0636\u0631\u0648\u0631\u064a \u0644\u0644\u062d\u0642<\/p>\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\u0627\u0644\u0637\u0627\u0626\u0631\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u062a\u0643\u0648\u0646 \u0645\u062a\u0648\u0627\u0632\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-5ce940060c57c2eae41e79fb31db1afe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ (x,y,z) = (2,0-1)+t(4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" 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-2f733e6dda28d7a2ab79930a2e311d76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 4x+3y+kz+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"194\" 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\u064b\u060c \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u062e\u0637 \u0643\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u062a\u062c\u0647\u0629\u060c \u0644\u0630\u0627 \u0641\u0625\u0646 \u0645\u062a\u062c\u0647 \u0627\u062a\u062c\u0627\u0647\u0647 \u0647\u0648:<\/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-d80ac01e619cde85001850e17e3f2bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" 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 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0639\u0644\u0649 \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0639\u0627\u0645\u0629\u060c \u0644\u0630\u0627 \u0641\u0625\u0646 \u0645\u062a\u062c\u0647\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0647\u0648:<\/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-b4a7ab8f96745e213fbc290625f5b463_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646\u060c \u0644\u0643\u064a \u064a\u0643\u0648\u0646 \u0627\u0644\u0639\u0646\u0635\u0631\u0627\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u064a\u062c\u0628 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 \u0635\u0641\u0631\u064b\u0627. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/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-efc7281925b7c514913e4aaf9102d342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(0\u00ba) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"133\" style=\"vertical-align: -17px;\"><\/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-240cba5c3a27806488b1e8172b55b8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" style=\"vertical-align: -17px;\"><\/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-61e18ce576fafff8b4db05f6bca9cedb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert =\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" 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-4639b105473c348e32b6d87593e0ab31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\vv{\\text{v}}_r \\cdot \\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062b\u0645\u060c \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0628\u064a\u0646 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0627\u062f\u064a \u0635\u0641\u0631\u064b\u0627. \u0648\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062d\u062f\u064a\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u062c\u0647\u0648\u0644 <\/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-7cf6d2c84f82625cb8a795ee1394251f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" 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-7dd4a6abbc2ab11fe54f43b6aeea5ee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(4,-1,3) \\cdot (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" 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-ecedbfc73f2ae09aa2f20d886b76217a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =4\\cdot 4 -1\\cdot 3 +3 \\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"168\" 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-d6b2fc367d696e22656777d9c8394f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =16 -3 +3 k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"120\" 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-14bd0daaa168493c0978bdec5f548829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -3k =13\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-27a35752a178021d706238eff36fe7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k =\\cfrac{13}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" 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-0aef8d9f84e0eeb1eceb52873846ca57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =-}\\mathbf{\\cfrac{13}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" 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<p style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0625\u0630\u0627 \u0648\u062c\u062f\u062a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u0641\u064a\u062f\u0629\u060c \u0641\u0645\u0646 \u0627\u0644\u0645\u062d\u062a\u0645\u0644 \u0623\u0646\u0643 \u0645\u0647\u062a\u0645 \u0623\u064a\u0636\u064b\u0627 \u0628\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0632\u0627\u0648\u064a\u0629-\u0628\u064a\u0646-\u0637\u0627\u064a\u0654\u0631\u062a\u064a\u0646-\u0641\u064a-\u0627\u0644\u0635\u064a\u063a\u0629-\u0627\u0644\u0641\u0636\u0627\u064a\u0654\u064a\u0629-r3\/\">\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646<\/a> . \u0633\u062a\u062c\u062f \u0641\u064a \u0635\u0641\u062d\u0629 \u0627\u0644\u0631\u0648\u0627\u0628\u0637 \u0634\u0631\u062d\u064b\u0627 \u0645\u0641\u0635\u0644\u064b\u0627 \u0644\u0644\u063a\u0627\u064a\u0629 \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646\u060c \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\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u064a\u0628 \u0648\u0627\u0644\u0641\u0647\u0645 \u0643\u064a\u0641 \u064a\u062a\u0645 \u0630\u0644\u0643 \u0639\u0644\u0649 \u0623\u0643\u0645\u0644 \u0648\u062c\u0647.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0633\u062a\u062a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u062d\u0648\u0644 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a. \u0645\u0627 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0637\u0627\u0626\u0631\u0629\u061f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0625\u0633\u0642\u0627\u0637\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u064a \u062a\u0643\u0645\u0644\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%b9%d9%84%d9%89-%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%a7%d9%84%d8%ae%d8%b7-%d9%88%d8%a7%d9%84%d9%85%d8%b3%d8%aa\/\"> <span class=\"screen-reader-text\">\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649<\/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-274","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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\u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0633\u062a\u062a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u062d\u0648\u0644 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0637 \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a. \u0645\u0627 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637 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