{"id":253,"date":"2023-07-10T11:53:09","date_gmt":"2023-07-10T11:53:09","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%b7%d8%a7%d8%a6%d8%b1%d8%aa%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a6%d9%8a\/"},"modified":"2023-07-10T11:53:09","modified_gmt":"2023-07-10T11:53:09","slug":"%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%b7%d8%a7%d8%a6%d8%b1%d8%aa%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a6%d9%8a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%b7%d8%a7%d8%a6%d8%b1%d8%aa%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a6%d9%8a\/","title":{"rendered":"\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\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\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629). \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 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-104\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-dos-planos\"><\/span> \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0645\u062a\u0643\u0627\u0641\u0626\u0629.<\/strong> <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-105\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0628\u0627\u0644\u0636\u0628\u0637 \u0645\u0627 \u0647\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0644\u0642\u064a \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 \u0635\u064a\u063a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3)\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627 \u0645\u0646 <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\/\">\u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646<\/a> : <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\u064a\u0629) \u0644\u0637\u0627\u0626\u0631\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-dfa3d7e6f1ece8353327be7c9227d75b_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-2c3966346685421fe3e535cf57a5491d_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:left;text-align:right;direction:rtl\"> \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0643\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-eb0ca06882e0d61d6f8134368946ef29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1=(A_1,B_1,C_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" 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-22fba6a063a544bdf257e64d8d139238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2=(A_2,B_2,C_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0648\u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0647\u0627\u062a\u0627\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u062a\u0627\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0625\u062a\u0642\u0627\u0646 \u062d\u0633\u0627\u0628 <a href=\"https:\/\/mathority.org\/ar\/\u062d\u0633\u0627\u0628-\u0627\u0644\u0645\u0646\u062a\u062c-\u0627\u0644\u0642\u064a\u0627\u0633\u064a-\u0628\u064a\u0646-\u0627\u062b\u0646\u064a\u0646-\u0645\u0646-\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a-\u0627\u0654\u0645\u062b\u0644\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0644\u0645\u062a\u062c\u0647\u064a\u0646<\/a> . \u0625\u0630\u0627 \u0643\u0646\u062a \u0644\u0627 \u062a\u062a\u0630\u0643\u0631 \u0643\u064a\u0641 \u062a\u0645 \u0630\u0644\u0643\u060c \u0641\u0633\u062a\u062c\u062f \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u062e\u0637\u0648\u0627\u062a \u062d\u0644 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646. \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.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646 \u0623\u0648 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629\u060c \u0644\u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u0628\u0627\u0634\u0631\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 <strong>\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646<\/strong> \u0647\u064a 0 \u062f\u0631\u062c\u0629\u060c \u0644\u0623\u0646 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0645\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 <strong>\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646<\/strong> \u0647\u064a 90 \u062f\u0631\u062c\u0629\u060c \u0644\u0623\u0646 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0623\u064a\u0636\u064b\u0627 (\u0623\u0648 \u0645\u062a\u0639\u0627\u0645\u062f\u0629) \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u0634\u0643\u0644 \u0632\u0627\u0648\u064a\u0629 \u0642\u0627\u0626\u0645\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-dos-planos\"><\/span> \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-106\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0645\u062b\u0627\u0644 \u0645\u0644\u0645\u0648\u0633 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0645\u0639\u0631\u0641\u0629 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646:<\/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 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646:<\/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-60b094e253552cbfa84175e60ef18801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-5y+z+4=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\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-364b525ebfd0b5ef85128562d1641cb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 4x+2y+3z-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\"> \u0623\u0648\u0644 \u0645\u0627 \u0639\u0644\u064a\u0646\u0627 \u0641\u0639\u0644\u0647 \u0647\u0648 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a X \u0648Y \u0648Z \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u062a\u0637\u0627\u0628\u0642 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0645\u0639 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\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-17c8988d3ee87dd9e708e46aadbb9086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (3,-5,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-5783f55ed327128d1da574f38c8336e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (4,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649\u060c \u0646\u062d\u0633\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0648\u0646\u0647\u0627 \u0628\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u062d\u062c\u0645 \u0643\u0644 \u0645\u062a\u062c\u0647 \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-96718e6e72f0f3045ee39364f636b419_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+(-5)^2+1^2}= \\sqrt{9+25+1} = \\sqrt{35}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/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-e3558cfa79b7113b469df5b36e00f1ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{4^2+2^2+3^2}= \\sqrt{16+4+9} = \\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"280\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0639\u0648\u0636 \u0628\u0642\u064a\u0645\u0629 \u0643\u0644 \u0645\u062c\u0647\u0648\u0644 \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-5cdc9e54b22394cf29f35c6c26ee1308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (3,-5,1) \\cdot (4,2,3)\\rvert}{\\sqrt{35} \\cdot \\sqrt{29} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0644 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a \u0644\u0644\u0645\u062a\u062c\u0647\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-b1923cb6ac441ba0e980bc984bc4804b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 3\\cdot 4 + (-5)\\cdot 2 +1 \\cdot 3 \\rvert}{\\sqrt{35}\\cdot \\sqrt{29} }=\\cfrac{\\lvert 12-10+3 \\rvert}{\\sqrt{1015}}= \\cfrac{5}{31,86}=0,16\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"497\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u062f\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u0645\u0639\u0643\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\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-57297e96c6a14eed6ff87abfe7699df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,16)=\\bm{80,97\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" 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=\"ejercicios-resueltos-del-angulo-entre-dos-planos\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-109\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\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\u0645\u062d\u0635\u0648\u0631\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-ac5eb1f4c801eae9ea93342c56e7aa60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+2z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"151\" style=\"vertical-align: -3px;\"><\/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-f7b262c6e50b562858b1c5043548ba75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+y-4z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" 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 \u0645\u0627 \u0639\u0644\u064a\u0646\u0627 \u0641\u0639\u0644\u0647 \u0647\u0648 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a X \u0648Y \u0648Z \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u0639\u0627\u062f\u0644 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\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-ef6a043fab595442ed8b17da7798fc34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (1,0,2)\" 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-158dadd8329a3954114f9d99160e9800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (3,1,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649\u060c \u0646\u062d\u0633\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u062d\u062c\u0645 \u0643\u0644 \u0645\u062a\u062c\u0647 \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-303393672cb4ca6c891bfcf49d3e30b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{1^2+0^2+2^2}= \\sqrt{1+4} = \\sqrt{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -3px;\"><\/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-ede42afce2c7b11dd96617df978ee401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+1^2+(-4)^2}= \\sqrt{9+1+16} = \\sqrt{26}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0639\u0648\u0636 \u0628\u0642\u064a\u0645\u0629 \u0643\u0644 \u0645\u062c\u0647\u0648\u0644 \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-90594e9bdf100d52e0221a86d0878d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (1,0,2) \\cdot (3,1,-4)\\rvert}{\\sqrt{5} \\cdot \\sqrt{26} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \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-fb411278d0746c45c8ef0490e51862b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 1\\cdot 3 + 0\\cdot 1 +2 \\cdot (-4) \\rvert}{\\sqrt{5}\\cdot \\sqrt{26} }=\\cfrac{\\lvert 3-8 \\rvert}{\\sqrt{130}}= \\cfrac{5}{11,4}=0,44\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"440\" style=\"vertical-align: -16px;\"><\/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\u062c\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0642\u0644\u0628 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\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-aa9117c27a8c072f275a8cb5fac99528_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,44)=\\bm{63,99\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" 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\"> \u0645\u0627 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u062d\u0635\u0648\u0631\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646\u061f <\/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-7566850c5f664f60ba826bb1ffbf7a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-2y+5z=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"170\" 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-ead661dfbeded4be15602ccda3f2864c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 6x+3y-z-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" 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 \u0645\u0627 \u0639\u0644\u064a\u0646\u0627 \u0641\u0639\u0644\u0647 \u0647\u0648 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a X \u0648Y \u0648Z \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u0633\u0627\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0645\u0646\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-54788d8fdba6722dc87ae3c06c350400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (3,-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-f6dee74c50bac2e8859c3f4a3c9742f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (6,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0643\u0644 \u0645\u0633\u062a\u0648\u0649\u060c \u0646\u062d\u0633\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u062d\u062c\u0645 \u0643\u0644 \u0645\u062a\u062c\u0647 \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-06daed2734e23937ffc63d52314656ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{3^2+(-2)^2+5^2}= \\sqrt{9+4+25} = \\sqrt{38}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/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-0f0bafe4966148f6e199dbd2bdc7ede1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{6^2+3^2+(-1)^2}= \\sqrt{36+9+1} = \\sqrt{46}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0639\u0648\u0636 \u0628\u0642\u064a\u0645\u0629 \u0643\u0644 \u0645\u062a\u063a\u064a\u0631 \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-3d635cbe5718a970df439157ca6346cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}=\\cfrac{\\lvert (3,-2,5) \\cdot (6,3,-1)\\rvert}{\\sqrt{38} \\cdot \\sqrt{46} }\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"332\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \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-a24e1ac8ad5f23b1d0734a564fa92a90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert 3\\cdot 6 + (-2)\\cdot 3 +5 \\cdot (-1) \\rvert}{\\sqrt{38}\\cdot \\sqrt{46} }=\\cfrac{\\lvert 18-6-5 \\rvert}{\\sqrt{1748}}= \\cfrac{7}{41,81}=0,17\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"516\" style=\"vertical-align: -16px;\"><\/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\u062d\u062f\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0642\u0644\u0628 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\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-d8fddc88af864b95ff37c56b126af7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\alpha = \\cos^{-1}(0,17)=\\bm{80,36\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" 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\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0627\u0628 \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0639\u0644\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> \u0628\u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\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-faed0ccf5807a84f20057b0128bbcee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+2y-3z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" 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-9872d7160fb07e1a3ca43e18e24b3435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -2x+5y+kz+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"215\" 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\u064b\u0627\u060c \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a\u060c \u0639\u0644\u064a\u0643 \u062f\u0627\u0626\u0645\u064b\u0627 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0643\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-add7176bfadc88b0c27dd09e33b340cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 = (1,2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-a3f04e685fb9ce2300340f149aa93059_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 = (-2,5,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062a\u0634\u0643\u0644 \u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u062a\u0627\u0646 \u0632\u0627\u0648\u064a\u0629 \u0642\u062f\u0631\u0647\u0627 90 \u062f\u0631\u062c\u0629\u060c \u0644\u0630\u0627 \u0641\u0625\u0646 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0645\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0623\u064a\u0636\u064b\u0627 90 \u062f\u0631\u062c\u0629. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \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-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> \u0645\u0639 \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\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-48fc901ce118ca0f0daecdf37b011101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"145\" 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-a35dde3971efe5cdf36340847dcb02e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(90\u00ba) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"151\" 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-eb4652afcc23693b300da306909293ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"104\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u0642\u0627\u0645 \u0627\u0644\u0643\u0633\u0631 \u064a\u0642\u0633\u0645 \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0645\u0646 \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u062d\u062a\u0649 \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u062a\u0645\u0631\u064a\u0631\u0647 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u0636\u0631\u0628 \u0641\u064a \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0622\u062e\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-f94a174ae36525a6e6ef055e53bb154a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert =\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"172\" 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-e4cffd0cb6eef3c14b8924706cca4a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\vv{n}_1 \\cdot \\vv{n}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0627\u0644\u0622\u0646 \u0646\u0648\u062c\u062f \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0639\u0627\u062f\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-3818384c903fe4f03fd785f0fbfb0197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(1,2,-3) \\cdot (-2,5,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"185\" 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-a0317a3a3ce7f7a3b19d199026305b93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =1 \\cdot (-2) + 2\\cdot 5 +(-3)\\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"223\" 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-c9a5497303548b34fd3bba83bdc588b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =-2 +10-3k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"134\" 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-3f68c05212b2541bc6d1142287eebc18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =8-3k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u0648\u0636\u062d \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-5c13e299367327b12f0f781a10c47f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 3k=8\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-b126ac6d6422d2ae3c536589c2461e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =}\\mathbf{\\cfrac{8}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" 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","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629). \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 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627. \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0645\u062a\u0643\u0627\u0641\u0626\u0629. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d8%b7%d8%a7%d8%a6%d8%b1%d8%aa%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d8%b5%d9%8a%d8%ba%d8%a9-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a6%d9%8a\/\"> <span class=\"screen-reader-text\">\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629)<\/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-253","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629) - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0632\u0627\u0648\u064a\u0629-\u0628\u064a\u0646-\u0637\u0627\u0626\u0631\u062a\u064a\u0646-\u0641\u064a-\u0627\u0644\u0635\u064a\u063a\u0629-\u0627\u0644\u0641\u0636\u0627\u0626\u064a\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629) - Mathority\" \/>\n<meta property=\"og:description\" content=\"\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0637\u0627\u0626\u0631\u062a\u0627\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629). \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 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627. \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0637\u0627\u0626\u0631\u062a\u064a\u0646 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0639\u0627\u062f\u064a\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0627\u062a \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u062f\u064a\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0645\u062a\u0643\u0627\u0641\u0626\u0629. &hellip; \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u0633\u062a\u0648\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0627\u0644\u0635\u064a\u063a\u0629) \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0632\u0627\u0648\u064a\u0629-\u0628\u064a\u0646-\u0637\u0627\u0626\u0631\u062a\u064a\u0646-\u0641\u064a-\u0627\u0644\u0635\u064a\u063a\u0629-\u0627\u0644\u0641\u0636\u0627\u0626\u064a\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T11:53:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dfa3d7e6f1ece8353327be7c9227d75b_l3.png\" \/>\n<meta name=\"author\" content=\"\u0641\u0631\u064a\u0642 Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0643\u064f\u062a\u0628 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