{"id":259,"date":"2023-07-10T08:56:34","date_gmt":"2023-07-10T08:56:34","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d8%a8%d9%8a%d9%86-%d8%ae%d8%b7%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1-%d9%81%d9%8a-r3\/"},"modified":"2023-07-10T08:56:34","modified_gmt":"2023-07-10T08:56:34","slug":"%d8%a7%d9%84%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d8%a8%d9%8a%d9%86-%d8%ae%d8%b7%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1-%d9%81%d9%8a-r3","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d8%a8%d9%8a%d9%86-%d8%ae%d8%b7%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1-%d9%81%d9%8a-r3\/","title":{"rendered":"\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a r3)"},"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\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3)\u060c \u0645\u0647\u0645\u0627 \u0643\u0627\u0646 \u0646\u0648\u0639\u0647\u0627 (\u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629\u060c \u0642\u0627\u0637\u0639\u0629\u060c \u0645\u062a\u0637\u0627\u0628\u0642\u0629\u060c \u0642\u0627\u0637\u0639\u0629\u060c \u0645\u062a\u0639\u0627\u0645\u062f\u0629\u060c \u0625\u0644\u062e). \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<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=\"como-calcular-la-distancia-entre-dos-rectas\"><\/span> \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\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-105\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0647\u064a \u0623\u0635\u063a\u0631 \u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0623\u062d\u062f \u0627\u0644\u062e\u0637\u064a\u0646 \u0648\u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0622\u062e\u0631. \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u062a\u0642\u0627\u0628\u0644 \u0637\u0648\u0644 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u0642\u0644 \u0645\u0646 \u062e\u0637 \u0625\u0644\u0649 \u0622\u062e\u0631 \u0648\u062a\u0643\u0648\u0646 \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0648\u0642\u062a \u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0645\u0639 \u0643\u0644\u0627 \u0627\u0644\u062e\u0637\u064a\u0646. <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/distance-entre-deux-lignes-dans-lespace-2.webp\" alt=\"\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3)\" class=\"wp-image-3056\" width=\"387\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0641\u0625\u0646 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0628\u064a\u0646\u0647\u0645\u0627:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 <strong>\u062a\u0637\u0627\u0628\u0642<\/strong> \u0627\u0644\u062e\u0637\u0627\u0646 \u0623\u0648 <strong>\u062a\u0642\u0627\u0637\u0639\u0627<\/strong> \u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u062a\u0643\u0648\u0646 \u0635\u0641\u0631\u0627\u064b\u060c \u0644\u0623\u0646\u0647\u0645\u0627 \u064a\u062a\u0642\u0627\u0637\u0639\u0627\u0646 (\u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644) \u0641\u064a \u0646\u0642\u0637\u0629 \u0648\u0627\u062d\u062f\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u062e\u0637\u0627\u0646 <strong>\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646<\/strong> \u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0623\u062e\u0630 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0623\u062d\u062f \u0627\u0644\u062e\u0637\u064a\u0646 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u0627\u0644\u062e\u0637 \u0627\u0644\u0622\u062e\u0631 (\u0623\u062f\u0646\u0627\u0647 \u0644\u062f\u064a\u0643 \u0645\u062b\u0627\u0644 \u0644\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643).<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 <strong>\u062a\u0642\u0627\u0637\u0639<\/strong> \u0627\u0644\u062e\u0637\u0627\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 (\u0627\u0646\u0638\u0631 \u0623\u062f\u0646\u0627\u0647 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0634\u0631\u062d \u0645\u0641\u0635\u0644).<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0623\u0648\u0644\u0627\u064b \u0645\u0639\u0631\u0641\u0629 \u0646\u0648\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u062b\u0645\u060c \u062d\u0633\u0628 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0627\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0623\u0648 \u0623\u062e\u0631\u0649. \u0644\u0630\u0644\u0643\u060c \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0623\u0646 \u062a\u062a\u0642\u0646 \u0628\u0627\u0644\u0641\u0639\u0644 <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0645\u0648\u0636\u0639-\u0627\u0644\u0646\u0633\u0628\u064a-\u0644\u062e\u0637\u064a\u0646-\u0641\u064a-\u0627\u0644\u0641\u0636\u0627\u0621-r3-\u0627\u0654\u0645\u062b\u0644\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0646\u0633\u0628\u064a \u0644\u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621<\/a> \u0642\u0628\u0644 \u0627\u0644\u0645\u062a\u0627\u0628\u0639\u0629\u060c \u0648\u0644\u0643\u0646 \u0625\u0630\u0627 \u0643\u0646\u062a \u0644\u0627 \u062a\u062a\u0630\u0643\u0631 \u0643\u064a\u0641 \u062a\u0645 \u0630\u0644\u0643 \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u0633\u062a\u0631\u0649 \u0634\u0631\u062d\u064b\u0627 \u0643\u0627\u0645\u0644\u0627\u064b \u0644\u0644\u063a\u0627\u064a\u0629 \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0623\u0645\u062b\u0644\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"como-hallar-la-distancia-entre-dos-rectas-paralelas-en-el-espacio\"><\/span> \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 <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\"> \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3) \u0628\u0646\u0641\u0633 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0643\u0645\u0627 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (\u0641\u064a R2): <strong>\u0639\u0644\u064a\u0643 \u0623\u0646 \u062a\u0623\u062e\u0630 \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0623\u064a \u0645\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0648\u062a\u062c\u062f \u0645\u0633\u0627\u0641\u0629 \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0622\u062e\u0631 \u062e\u0637.<\/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\/distance-entre-un-point-et-une-ligne-en-ligne.webp\" alt=\"\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\" class=\"wp-image-1960\" width=\"425\" height=\"361\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; 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\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u062e\u0637 \u0641\u064a \u062b\u0644\u0627\u062b\u0629 \u0623\u0628\u0639\u0627\u062f (\u0648\u0627\u0644\u062a\u064a \u062a\u0633\u062a\u062e\u062f\u0645 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646) \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-7c7a838a254403e912767fb131474703_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"225\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px;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-74f213a2a0ca1a22659ce06a80bc5d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}}_r \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0647\u0648 \u062d\u062c\u0645 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c758bec4c272382411b95fc0e7ee250_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0647\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0633\u0637\u0631<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42ca8c420951296e93092e708435813a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0627\u0644\u0633\u0637\u0631<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdca087897cc5ad573be7ce2b595dfb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062d\u062f\u062f \u0628\u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646<\/li>\n<li style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de23c83cb189398d246990817a7e83db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0647\u0648 \u062d\u062c\u0645 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdca087897cc5ad573be7ce2b595dfb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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<\/li>\n<\/ul>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u0642\u0648\u0645 \u0628\u062d\u0644 \u0645\u0633\u0623\u0644\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0627 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646\u061f <\/li>\n<\/ul>\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<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-43cb370e9b16d006262ec6893e02dc92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ (x,y,z) = (2,1,1) + t(-1,3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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-48307ac3d4d0b23d6816a7473b6b1c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\ (x,y,z) = (-2,4,1) + t(2,-6,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0643\u0644\u0627 \u0627\u0644\u062e\u0637\u064a\u0646 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u062a\u062c\u0647\u0629\u060c \u0644\u0630\u0644\u0643 \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0633\u0647\u0648\u0644\u0629 \u0645\u0639\u0631\u0641\u0629 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0643\u0644 \u0645\u0646\u0647\u0645\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91c721e906a848c6c129721fe7908112_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r : \\ \\begin{cases}\\vv{\\text{v}}_r=(-1,3,2) \\\\[1.7ex] Q(2,1,1) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases}\\vv{\\text{v}}_s=(2,-6,-4) \\\\[1.7ex] P(-2,4,1) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0644\u062f\u064a\u0643 \u0623\u064a \u0634\u0643\u0648\u0643 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0627\u0644\u062e\u0637\u060c \u0646\u0646\u0635\u062d\u0643 \u0628\u0625\u0644\u0642\u0627\u0621 \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 \u0634\u0631\u062d <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a-\u0627\u0644\u062e\u0637\u064a\u0629-\u062c\u0645\u064a\u0639-\u0627\u0644\u0635\u064a\u063a-\u0648\u0627\u0644\u0627\u0654\u0645\u062b\u0644\u0629-\u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646-\u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637<\/a> . \u0644\u0642\u062f \u0634\u0631\u062d\u0646\u0627 \u0630\u0644\u0643 \u0644\u062c\u0645\u064a\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u060c \u0644\u0623\u0646 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0646\u0648\u0639 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0641\u064a\u0647\u0627 \u0639\u0646 \u0627\u0644\u062e\u0637.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646\u060c \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646\u060c \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0625\u0644\u0649 \u062e\u0637 \u0645\u0633\u062a\u0642\u064a\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c7a838a254403e912767fb131474703_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"225\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u062d\u0633\u0628 \u0648\u062d\u062f\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0644\u062f\u064a\u0643 \u0634\u0643\u0648\u0643 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0631\u062c\u0648\u0639 \u0625\u0644\u0649 <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0654\u0645\u062b\u0644\u0629-\u0639\u0644\u0649-\u0627\u0644\u0645\u0646\u062a\u062c-\u0627\u0644\u0627\u062a\u062c\u0627\u0647\u064a-\u0644\u0645\u062a\u062c\u0647\u064a\u0646-\u0648\u0627\u0644\u0635\u064a\u063a\u0629-\u0627\u0644\u062a\u0628\u0627\u062f\u0644\u064a\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u062c\u0647<\/a> \u060c \u062d\u064a\u062b\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 \u0644\u0647\u0630\u0647 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\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-dadf92e90a88ce334cf34bce072e5457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP} = Q - P = (2,1,1)-(-2,4,1) = (4,-3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-f166cb84d794adae8b8e5678790a5ad8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP} \\times \\vv{\\text{v}}_r  =\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k}  \\\\[1.1ex] 4&amp;-3&amp;0 \\\\[1.1ex] -1&amp;3&amp;2 \\end{vmatrix}=-6\\vv{i} -8\\vv{j}+9\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"316\" 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-bcf2fce752d73d75254674158d4824b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\vv{QP} \\times \\vv{\\text{v}}_r \\right| =\\sqrt{(-6)^2+(-8)^2+9^2} = \\sqrt{36+64+81} = \\sqrt{181}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"464\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u062c\u062f \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u062c\u0647 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-beb8af5ebd61faa6a707fabf3a13de60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}}_r \\rvert = \\sqrt{(-1)^2+3^2+2^2} = \\sqrt{1+9+4} = \\sqrt{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"351\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0648\u0636 \u0628\u0642\u064a\u0645\u0629 \u0643\u0644 \u062d\u062f \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u0648\u0646\u062d\u0633\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0633\u0637\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-dfc98500cdf36f3b5f09c525579f7f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}=\\cfrac{\\sqrt{181}}{\\sqrt{14}} = \\bm{3,60}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"350\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062b\u0645\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0647\u064a 3.60 \u0648\u062d\u062f\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"como-determinar-la-distancia-entre-dos-rectas-que-se-cruzan-en-el-espacio\"><\/span> \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629\u060c \u0641\u0625\u0646 \u0637\u0631\u064a\u0642\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 \u062a\u062e\u062a\u0644\u0641 \u0639\u0646 \u0637\u0631\u064a\u0642\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629. <\/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\/lignes-dintersection-1.webp\" alt=\"\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639\u0629 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\" class=\"wp-image-2692\" width=\"226\" height=\"221\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0647\u0646\u0627\u0643 \u0639\u062f\u0629 \u0637\u0631\u0642 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0633\u0646\u0634\u0631\u062d \u0625\u062c\u0631\u0627\u0621 \u0648\u0627\u062d\u062f \u0641\u0642\u0637\u060c \u0648\u0647\u0648 \u0627\u0644\u0623\u0628\u0633\u0637\u060c \u0644\u0623\u0646 \u0627\u0644\u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0627\u0644\u0623\u062e\u0631\u064a\u064a\u0646 \u0623\u0637\u0648\u0644 \u0648\u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u064b\u0627\u060c \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0644\u0627 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0645\u0627 \u0639\u0645\u0644\u064a\u064b\u0627. <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; 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\"> \u0644\u064a\u0643\u0646 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0623\u064a \u0646\u0642\u0637\u0629 \u0645\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\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-569f8d554a0f3704d247862d0b8ef852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} \\\\[2ex] A\\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}} \\\\[2ex] B\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"210\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;text-align:right;direction:rtl\"> <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646<\/strong> \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dbc3e38427d29b2f4444ea732f955500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0647\u064a \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0642\u0629 \u0644\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062e\u062a\u0644\u0637 \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0648\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u062d\u062f\u062f \u0628\u0627\u0644\u0646\u0642\u0627\u0637<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> . \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a151f35eca7cc81494de906050e773fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0647\u064a \u0633\u0639\u0629 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637\u064a\u0646 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646.<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0643\u064a \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0645\u0639\u0631\u0641\u0629 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646\u060c \u0633\u0646\u062d\u0644 \u0645\u0633\u0623\u0644\u0629 \u0643\u0645\u062b\u0627\u0644:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0627 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646\u061f<\/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-6c4b9507f6e33691e0b89d18dac941cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  \\cfrac{x-1}{2} = \\cfrac{y-2}{4} = \\cfrac{z+2}{-1}\" 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-c6dac5d90c57534aa97625685e0d60fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\  \\cfrac{x-3}{1} = \\cfrac{y+1}{3} = \\cfrac{z-1}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u064b\u0627\u060c \u0639\u0644\u064a\u0646\u0627 \u062a\u062d\u062f\u064a\u062f \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0643\u0644 \u062e\u0637. \u0648\u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u062e\u0637\u064a\u0646 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629\u060c \u0648\u0628\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-8b990f78d0263975304586abbd330167_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(2,4,-1) \\\\[2ex] A(1,2,-2) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(1,3,-2) \\\\[2ex] B(3,-1,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0646\u062d\u0644 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062e\u062a\u0644\u0637 (\u0623\u0648 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0639\u062f\u062f\u064a \u0627\u0644\u062b\u0644\u0627\u062b\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-3238f24b114cb49bf33dd66bccad1ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (3,-1,1) - (1,2,-2) = (2,-3,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" 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-c52c12945d04e320e688caf714569113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\\\[1.1ex] 2&amp;-3&amp;3 \\end{vmatrix}\\right| = \\left| -13 \\right| =13\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"321\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u062c\u062f \u0648\u062d\u062f\u0629 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0627\u062a\u062c\u0627\u0647\u064a (\u0623\u0648 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0627\u062a\u062c\u0627\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-71afa7d4b49e542300c12b5263858665_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}} =\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\end{vmatrix}=-5\\vv{i} +3\\vv{j}+2\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"278\" 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-3c940dca4c85f7176555de5861b8f391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{5^2+3^2+2^2} = \\sqrt{25+9+4} = \\sqrt{38}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0648\u0636 \u0628\u0642\u064a\u0645\u0629 \u0643\u0644 \u062d\u062f \u0641\u064a \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0645\u062a\u0642\u0627\u0637\u0639\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-b0aac39997c35738e8e84a29ff7c97c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{13}{\\sqrt{38}}= \\bm{2,11}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"273\" style=\"vertical-align: -17px;\"><\/p><\/p>\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\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3)\u060c \u0645\u0647\u0645\u0627 \u0643\u0627\u0646 \u0646\u0648\u0639\u0647\u0627 (\u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629\u060c \u0642\u0627\u0637\u0639\u0629\u060c \u0645\u062a\u0637\u0627\u0628\u0642\u0629\u060c \u0642\u0627\u0637\u0639\u0629\u060c \u0645\u062a\u0639\u0627\u0645\u062f\u0629\u060c \u0625\u0644\u062e). \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. \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0647\u064a \u0623\u0635\u063a\u0631 \u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0623\u064a \u0646\u0642\u0637\u0629 \u0639\u0644\u0649 \u0623\u062d\u062f \u0627\u0644\u062e\u0637\u064a\u0646 \u0648\u0623\u064a \u0646\u0642\u0637\u0629 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%a7%d9%84%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d8%a8%d9%8a%d9%86-%d8%ae%d8%b7%d9%8a%d9%86-%d9%81%d9%8a-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1-%d9%81%d9%8a-r3\/\"> <span class=\"screen-reader-text\">\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u062e\u0637\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a r3)<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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