{"id":272,"date":"2023-07-10T02:22:55","date_gmt":"2023-07-10T02:22:55","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%a7-%d9%87%d9%8a-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%a7%d9%84%d9%81%d9%8a%d8%b2%d9%8a%d8%a7%d8%a1-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87\/"},"modified":"2023-07-10T02:22:55","modified_gmt":"2023-07-10T02:22:55","slug":"%d9%85%d8%a7-%d9%87%d9%8a-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%a7%d9%84%d9%81%d9%8a%d8%b2%d9%8a%d8%a7%d8%a1-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%a7-%d9%87%d9%8a-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%a7%d9%84%d9%81%d9%8a%d8%b2%d9%8a%d8%a7%d8%a1-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87\/","title":{"rendered":"\u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a (\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a)\u061f"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629\u060c \u0633\u062a\u062c\u062f \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a: \u0645\u0627 \u0647\u064a\u060c \u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629\u060c&#8230;<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-vector\"><\/span> \u0645\u0627 \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c <strong>\u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0642\u0637\u0639\u0629 \u0645\u0648\u062c\u0647\u0629 \u062a\u0646\u062a\u0642\u0644 \u0645\u0646 \u0646\u0642\u0637\u0629 (\u062a\u0633\u0645\u0649 \u0627\u0644\u0623\u0635\u0644) \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 (\u062a\u0633\u0645\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0629).<\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0623\u062f\u0646\u0627\u0647\u060c \u064a\u0645\u0643\u0646\u0643 \u0623\u0646 \u062a\u0631\u0649 \u0623\u0646 \u0627\u0644\u0645\u062a\u062c\u0647<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-243865b783ec40e03ec861ac2ebcb279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0644\u0647\u0627 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0643\u0623\u0635\u0644\u0647\u0627 \u0648\u0627\u0644\u0646\u0642\u0637\u0629 B \u0643\u0646\u0642\u0637\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quest-ce-quun-vecteur.webp\" alt=\"\u0645\u0627 \u0647\u0648 \u0646\u0627\u0642\u0644 \u0631\u064a\u0627\u0636\u064a\" class=\"wp-image-3678\" width=\"176\" height=\"176\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0628\u0634\u0643\u0644 \u0623\u0633\u0627\u0633\u064a \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0648\u062e\u0627\u0635\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u0629 \u0628\u064a\u0627\u0646\u064a\u0627\u064b. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-un-vector\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0646\u0627\u0642\u0644\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0623\u0646 \u0631\u0623\u064a\u0646\u0627 \u0627\u0644\u0645\u0639\u0646\u0649 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0627\u0644\u0622\u0646 \u0645\u0627 \u0647\u064a \u062e\u0635\u0627\u0626\u0635\u0647\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0643\u0644 \u0645\u062a\u062c\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0627\u062a\u062c\u0627\u0647<\/strong> : \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647 \u0623\u0648 \u0623\u064a \u062e\u0637 \u0645\u0648\u0627\u0632 \u0644\u0647. \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u0642\u0639 \u0639\u0644\u064a\u0647.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0627\u062a\u062c\u0627\u0647<\/strong> : \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u060c \u0648\u064a\u0634\u0627\u0631 \u0625\u0644\u064a\u0647 \u0628\u0633\u0647\u0645\u0647.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0648\u062d\u062f\u0629<\/strong> (\u0623\u0648 \u0627\u0644\u062d\u062c\u0645): \u0648\u062d\u062f\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u064a \u0637\u0648\u0644\u0647\u060c \u0648\u062a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0644\u0644\u0645\u062a\u062c\u0647. \u0648\u0644\u0630\u0644\u0643\u060c \u0643\u0644\u0645\u0627 \u0632\u0627\u062f \u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u0632\u0627\u062f\u062a \u0643\u0645\u064a\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u064a \u064a\u0645\u062b\u0644\u0647\u0627.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0637\u0628\u064a\u0642<\/strong> : \u0646\u0642\u0637\u0629 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u064a \u0623\u0635\u0644 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0630\u0643\u0648\u0631. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/caracteristiques-d-un-vecteur.webp\" alt=\"\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a\" class=\"wp-image-3682\" width=\"332\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u063a\u0627\u0644\u0628\u064b\u0627 \u0645\u0627 \u062a\u0643\u0648\u0646 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0645\u0631\u0628\u0643\u0629\u060c \u0644\u0630\u0644\u0643 \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646\u0647\u0645\u0627. \u0627\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0645\u062a\u062c\u0647\u064a\u0646\u060c \u0643\u0644\u0627\u0647\u0645\u0627 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0644\u0643\u0646 \u0645\u0639\u0627\u0646\u064a\u0647\u0645\u0627 \u0645\u062e\u062a\u0644\u0641\u0629: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/sens-et-direction-d-un-vecteur.webp\" alt=\"\u0645\u0639\u0646\u0649 \u0645\u0639\u0646\u0649 \u0648\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647\" class=\"wp-image-3686\" width=\"446\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0623\u0646\u0647\u0645\u0627 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646. \u0648\u0628\u062f\u0644\u0627 \u0645\u0646 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u062a\u062c\u0627\u0647\u0627\u062a\u0647\u0645\u0627 \u0645\u0639\u0627\u0643\u0633\u0629 \u0644\u0623\u0646\u0647\u0645\u0627 \u064a\u0648\u0627\u062c\u0647\u0627\u0646 \u0627\u0644\u062e\u0644\u0641.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"componentes-de-un-vector\"><\/span> \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0642\u062f \u0631\u0623\u064a\u0646\u0627 \u0644\u0644\u062a\u0648 \u0623\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0628\u064a\u0627\u0646\u064a\u064b\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0623\u0633\u0647\u0645\u060c \u0648\u0644\u0643\u0646 \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0631\u0642\u0645\u064a\u064b\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0645\u0643\u0648\u0646\u0627\u062a (\u0623\u0648 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a) \u0627\u0644\u0645\u062a\u062c\u0647.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u0627\u0644\u064a \u0645\u0645\u062b\u0644\u064b\u0627 \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteur-exemples.webp\" alt=\"\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\" class=\"wp-image-3692\" width=\"316\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u064b\u0627 \u062a\u062d\u062f\u064a\u062f \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0623\u0635\u0644\u0647 \u0648\u0646\u0647\u0627\u064a\u062a\u0647\u060c \u0623\u064a \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u064a\u0628\u062f\u0623 \u0645\u0646\u0647\u0627 \u0648\u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u064a\u0646\u062a\u0647\u064a \u0641\u064a\u0647\u0627. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0623\u0635\u0644 \u0627\u0644\u0645\u062a\u062c\u0647 \u0648\u0646\u0647\u0627\u064a\u062a\u0647 \u0647\u0645\u0627:<\/p>\n<p class=\"has-text-align-center\" style=\";text-align:right;direction:rtl\"> \u0623\u0635\u0644 \u0627\u0644\u0645\u062a\u062c\u0647: A(2,1)<\/p>\n<p class=\"has-text-align-center\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0637\u0629 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u062a\u062c\u0647: B(5,6)<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0623\u0648 \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0637\u0631\u062d \u0646\u0642\u0637\u0629 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0646\u0627\u0642\u0635 \u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u0635\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-fba10729c8ded7f7c7051cfda5c12eab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{AB} &amp; = B- A \\\\[2ex] &amp; = (5,6)- (2,1) \\\\[2ex] &amp;= (5-2 \\ , \\ 6-1) \\\\[2ex] &amp;= (3,5) \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"144\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0645\u062b\u0644\u0629 \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \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-8fbf31faea8cf602f9556fa80f618515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\bm{AB}}\\bm{=(3,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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=\"operaciones-con-vectores\"><\/span> \u0639\u0645\u0644\u064a\u0627\u062a \u0646\u0627\u0642\u0644\u0627\u062a <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"suma-de-vectores\"><\/span> \u0645\u0636\u064a\u0641\u0627 \u0646\u0627\u0642\u0644\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0625\u0636\u0627\u0641\u0629 \u0645\u062a\u062c\u0647\u064a\u0646 \u0639\u062f\u062f\u064a\u064b\u0627\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0625\u0636\u0627\u0641\u0629 \u0645\u0643\u0648\u0646\u0627\u062a \u0643\u0644 \u0645\u0646\u0647\u0645\u0627. \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u064a\u062a\u0645 \u0625\u0636\u0627\u0641\u0629 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a X \u0644\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0648\u0646\u0641\u0633 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a Y.<\/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-d97d089a143f6e30d987b0ed74c56dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} + \\vv{\\text{v}} = (\\text{u}_x + \\text{v}_x \\ , \\ \\text{u}_y + \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0633\u0646\u0636\u064a\u0641 \u0627\u0644\u0645\u062a\u062c\u0647\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-d5107f1a0b5a49b0ffd79eb20211c48b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (2,3) \\qquad \\vv{\\text{v}}=(4, -1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-24ac65138e4d395f7773aa19ba806a49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} + \\vv{\\text{v}}&amp; =(2,3) +(4,-1) \\\\[2ex] &amp; = (2+4,3+(-1)) \\\\[2ex] &amp; = \\bm{(6,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0625\u0636\u0627\u0641\u0629 \u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u0646 \u062a\u0645\u062b\u064a\u0644\u0627\u062a\u0647\u0645\u0627 \u0627\u0644\u0631\u0633\u0648\u0645\u064a\u0629. \u0644\u0647\u0630\u0627\u060c \u0639\u0627\u062f\u0629 \u0645\u0627 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u0623\u0648 \u0642\u0627\u0646\u0648\u0646 \u0645\u062a\u0648\u0627\u0632\u064a \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060c \u0648\u0644\u0643\u0646 \u0647\u0646\u0627\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0637\u0631\u0642. \u064a\u0645\u0643\u0646\u0643 \u0645\u0634\u0627\u0647\u062f\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 \u062d\u0648\u0644 <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0655\u0636\u0627\u0641\u0629-\u0645\u062c\u0645\u0648\u0639-\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a-\u0628\u064a\u0627\u0646\u064a\u0627-\u0648\u0627\u0654\u0645\u062b\u0644\u0629-\u0645\u062d\u0644\u0648\u0644\u0629-\u0639\u062f\u062f\u064a\u0627\/\">\u0643\u064a\u0641\u064a\u0629 \u0625\u0636\u0627\u0641\u0629 \u0645\u062a\u062c\u0647\u064a\u0646 \u0628\u064a\u0627\u0646\u064a\u064b\u0627<\/a> \u0647\u0646\u0627.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"resta-de-vectores\"><\/span> \u0637\u0631\u062d \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0637\u0631\u062d \u0645\u062a\u062c\u0647\u064a\u0646 \u062a\u062d\u0644\u064a\u0644\u064a\u064b\u0627\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0637\u0631\u062d \u0645\u0643\u0648\u0646\u0627\u062a \u0643\u0644 \u0645\u0646\u0647\u0645\u0627. \u0623\u064a \u0623\u0646\u0647 \u064a\u062a\u0645 \u0637\u0631\u062d \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a X \u0644\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u0646 \u0628\u0639\u0636\u0647\u0645\u0627 \u0627\u0644\u0628\u0639\u0636 \u0648\u0646\u0641\u0633 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a Y.<\/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-c755aca302ff1c1b956ca3d91bac1095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c} \\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y) \\qquad \\vv{\\text{v}}=(\\text{v}_x, \\text{v}_y)\\\\[4ex]\\vv{\\text{u}} - \\vv{\\text{v}} = (\\text{u}_x - \\text{v}_x \\ , \\ \\text{u}_y - \\text{v}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0648\u0641 \u0646\u0642\u0648\u0645 \u0628\u0637\u0631\u062d \u0627\u0644\u0645\u062a\u062c\u0647\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-0e6976699c55e7cb1372aca76313b056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,1) \\qquad \\vv{\\text{v}}=(2, -4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-5693a8287adebc3a4553358f8a8b0969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} - \\vv{\\text{v}}&amp; =(3,1) -(2,-4) \\\\[2ex] &amp; = (3-2,1-(-4)) \\\\[2ex]&amp; = (3-2,1+4) \\\\[2ex] &amp; = \\bm{(1,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0645\u0639 \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u062c\u0645\u0639\u060c \u064a\u0645\u0643\u0646\u0643 \u0623\u064a\u0636\u064b\u0627 \u0637\u0631\u062d \u0645\u062a\u062c\u0647\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0645\u062b\u064a\u0644\u0647\u0645\u0627. \u0644\u0647\u0630\u0627\u060c \u0639\u0627\u062f\u0629 \u0645\u0627 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u0623\u0648 \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0645\u062b\u0644\u062b\u060c \u0648\u0644\u0643\u0646 \u0647\u0646\u0627\u0643 \u0639\u062f\u0629 \u0637\u0631\u0642. \u064a\u0645\u0643\u0646\u0643 \u0631\u0624\u064a\u062a\u0647\u0627 \u062c\u0645\u064a\u0639\u064b\u0627 \u0645\u0639 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u062d\u0648\u0644 <a href=\"https:\/\/mathority.org\/ar\/\u0637\u0631\u062d-\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a-\u0639\u062f\u062f\u064a\u0627-\u0628\u064a\u0627\u0646\u064a\u0627-\u0627\u0654\u0645\u062b\u0644\u0629-\u062a\u0645\u0631\u064a\u0646-\u0637\u0631\u062d\/\">\u0643\u064a\u0641\u064a\u0629 \u0637\u0631\u062d \u0645\u062a\u062c\u0647\u064a\u0646 \u0628\u064a\u0627\u0646\u064a\u064b\u0627<\/a> .<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"modulo-de-un-vector\"><\/span> \u0648\u062d\u062f\u0629 \u0645\u0646 \u0646\u0627\u0642\u0644\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0641\u064a \u0628\u062f\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629\u060c \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647 \u064a\u0642\u0627\u0628\u0644 \u0637\u0648\u0644\u0647. \u062d\u0633\u0646\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0637\u0648\u0644 (\u0623\u0648 \u062d\u062c\u0645) \u0627\u0644\u0645\u062a\u062c\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u0643\u0648\u0646\u0627\u062a\u0647.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0646\u0638\u0631 \u0641\u064a \u0623\u064a \u0646\u0627\u0642\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-d4b2f8c9cdb09377a66fbce8392c30ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0625\u064a\u062c\u0627\u062f \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \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-95466c107aed66569925d4b89a3a939b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ \\text{u}_x^2+\\text{u}_y^2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0648\u0641 \u0646\u062d\u0633\u0628 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u0627\u0644\u064a \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-6273ca0b37b024bc5684ec07237607bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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-d78c0f573a5d2db399d099ebc4a3cb85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =\\sqrt{3^2+(-4)^2} = \\sqrt{9+16}=\\sqrt{25} = \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"316\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u0623\u0645\u0631 \u064a\u0628\u062f\u0648 \u0628\u0633\u064a\u0637\u064b\u0627 \u062c\u062f\u064b\u0627\u060c \u0625\u0644\u0627 \u0623\u0646 \u062a\u062d\u062f\u064a\u062f \u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0642\u062f \u064a\u0643\u0648\u0646 \u0645\u0639\u0642\u062f\u064b\u0627. \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0631\u064a\u062f \u0631\u0624\u064a\u0629 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u062f\u0631\u064a\u0628\u0627\u062a \u0639\u0644\u0649 <a href=\"https:\/\/mathority.org\/ar\/\u0648\u062d\u062f\u0629-\u0645\u0646-\u0635\u064a\u063a\u0629-\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c-\u0627\u0654\u0645\u062b\u0644\u0629-\u0639\u0644\u0649-\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646-\u0627\u0644\u062a\u064a-\u062a\u0645-\u062d\u0644\u0647\u0627\/\">\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u0644\u0648\u062d\u062f\u0629 \u0627\u0644\u0645\u062a\u062c\u0647<\/a> \u060c \u0641\u0646\u0648\u0635\u064a\u0643 \u0628\u0632\u064a\u0627\u0631\u0629 \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"multiplicacion-de-un-vector-por-un-escalar\"><\/span> \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f (\u0623\u0648 \u0639\u062f\u062f\u064a)\u060c \u064a\u062c\u0628 \u0636\u0631\u0628 \u0643\u0644 \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0647\u0630\u0627 \u0627\u0644\u0631\u0642\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-dc2018686141332d7620fe51d93dae8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\\\\[4ex]k\\cdot \\vv{\\text{u}} =(k\\cdot \\text{u}_x \\ , \\ k\\cdot \\text{u}_y) \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0639\u0627\u0645 \u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646\u0643 \u0623\u0646 \u062a\u0631\u0649 \u0643\u064a\u0641 \u064a\u062a\u0645 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629. \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0641\u0625\u0646 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0630\u064a \u064a\u0636\u0631\u0628\u0647. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/multiplication-ou-produit-dun-nombre-ou-dun-scalaire-par-un-vecteur.webp\" alt=\"\u0627\u0644\u0636\u0631\u0628 \u0623\u0648 \u0627\u0644\u0645\u0646\u062a\u062c \u0644\u0639\u062f\u062f \u0623\u0648 \u0639\u062f\u062f \u0642\u064a\u0627\u0633\u064a \u0628\u0648\u0627\u0633\u0637\u0629 \u0646\u0627\u0642\u0644\" class=\"wp-image-283\" width=\"298\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0643 \u0623\u062f\u0646\u0627\u0647 \u0631\u0624\u064a\u0629 \u0645\u062b\u0627\u0644 \u0639\u062f\u062f\u064a \u0644\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0646\u062a\u062c \u0645\u062a\u062c\u0647 \u0648\u0631\u0642\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-6c2dd0a37f737f7c82d6da8b971ca0f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} =(3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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-87282d0a06c534058bd4b64120bdf391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{\\text{u}} =(4 \\cdot 3 \\ , \\ 4 \\cdot (-2)) = \\bm{(12,-8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"producto-escalar\"><\/span> \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0639\u062f\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a \u0647\u0648 \u0639\u0645\u0644\u064a\u0629 \u0645\u062a\u062c\u0647\u0629 \u062a\u0642\u0648\u0645 \u0628\u0636\u0631\u0628 \u0645\u062a\u062c\u0647\u064a\u0646 \u0648\u062a\u062d\u0648\u064a\u0644\u0647\u0645\u0627 \u0625\u0644\u0649 \u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a \u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f09930024fc5c410889bea53d06982e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle  \\vv{\\text{u}} \\cdot \\vv{\\text{v}} = \\text{u}_x\\cdot \\text{v}_x + \\text{u}_y\\cdot \\text{v}_y \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0648\u062c\u062f \u0623\u062f\u0646\u0627\u0647 \u0645\u062b\u0627\u0644 \u062d\u064a\u062b \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \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-7437bf59c08f823d3a9ca8b5f32a3f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,2) \\qquad \\vv{\\text{v}} = (-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-d2a8137101f391be2b197764b8b21223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{aligned} \\vv{\\text{u}} \\cdot \\vv{\\text{v}}&amp;=(4,2)\\cdot (-1,3) \\\\[1.5ex]&amp;=4\\cdot (-1) + 2 \\cdot 3 \\\\[1.5ex] &amp; = -4+6  \\\\[1.5ex] &amp; =\\bm{10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0631\u0627\u0628\u0637 \u064a\u0645\u0643\u0646\u0643 \u0631\u0624\u064a\u0629 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 <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\/\">\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a<\/a> . \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0637\u0631\u064a\u0642\u0629 \u0623\u062e\u0631\u0649 \u0644\u0625\u064a\u062c\u0627\u062f \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646\u060c \u0648\u062e\u0635\u0627\u0626\u0635 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0645\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"producto-vectorial\"><\/span> \u0645\u0646\u062a\u062c \u0646\u0627\u0642\u0644\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646\u0647\u0645\u0627 \u0645\u062a\u0634\u0627\u0628\u0647\u0627\u0646 \u062c\u062f\u064b\u0627 \u0641\u064a \u0627\u0644\u0627\u0633\u0645\u060c \u0625\u0644\u0627 \u0623\u0646 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a \u0648\u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639 \u0645\u062e\u062a\u0644\u0641\u0627\u0646 \u062a\u0645\u0627\u0645\u064b\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639<\/strong> \u060c \u0648\u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639\u060c \u0647\u0648 \u0639\u0645\u0644\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 (\u0641\u064a R3)\u060c \u0623\u064a \u0623\u0646\u0647\u0645\u0627 \u0645\u062a\u062c\u0647\u0627\u0646 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0623\u064a \u0645\u062a\u062c\u0647\u064a\u0646 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f:<\/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-581394386a4c68ca2bfa92fb4e2445ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (\\text{u}_x,\\text{u}_y,\\text{u}_z) \\qquad \\vv{\\text{v}}= (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0646\u0627\u062a\u062c \u0627\u0644\u0627\u062a\u062c\u0627\u0647\u064a \u0644\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0645\u062d\u062f\u062f 3\u00d73 \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-6c85dc2dfb37842b31dea465c8887bc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\end{vmatrix}  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u064a\u062b \u0627\u0644\u0646\u0648\u0627\u0642\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-899f7cb82c85508ac2129e2393976f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}, \\vv{j},\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0647\u064a \u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0648\u062d\u062f\u0629 \u0641\u064a \u0627\u062a\u062c\u0627\u0647\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0648\u0631 X\u060c Y\u060c Z \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0646\u0627\u062a\u062c \u064a\u0643\u0648\u0646 \u0639\u0645\u0648\u062f\u064a\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0645\u0636\u0631\u0648\u0628\u064a\u0646.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u062a\u062e\u0645\u064a\u0646\u060c \u0641\u0625\u0646 \u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0623\u0643\u062b\u0631 \u0635\u0639\u0648\u0628\u0629 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628\u060c \u0644\u062f\u064a\u0646\u0627 \u0635\u0641\u062d\u0629 \u0643\u0627\u0645\u0644\u0629 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0634\u0631\u062d \u062a\u0641\u0635\u064a\u0644\u064a \u0644\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0627\u062a\u062c\u0627\u0647\u064a \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646. \u0644\u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u0645\u0647\u062a\u0645\u064b\u0627\u060c \u0641\u0646\u0648\u0635\u064a\u0643 \u0628\u0632\u064a\u0627\u0631\u062a\u0647 \u0648\u0627\u0644\u062a\u062f\u0631\u0628 \u0639\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\/\">\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627<\/a> .<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"producto-mixto\"><\/span> \u0645\u0646\u062a\u062c \u0645\u062e\u062a\u0644\u0637<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062e\u062a\u0644\u0637<\/strong> \u0644\u062b\u0644\u0627\u062b\u0629 \u0646\u0627\u0642\u0644\u0627\u062a\u060c \u0648\u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u060c \u0647\u0648 \u0636\u0631\u0628 \u0645\u062a\u062a\u0627\u0628\u0639 \u0628\u064a\u0646 \u062b\u0644\u0627\u062b\u0629 \u0645\u062a\u062c\u0647\u0627\u062a \u064a\u062a\u0636\u0645\u0646 \u0646\u0648\u0639\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a: \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0648\u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647. \u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u062a\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u062a\u064a\u0646 \u064a\u0639\u0637\u064a \u0631\u0642\u0645\u064b\u0627 \u0642\u064a\u0627\u0633\u064a\u064b\u0627 (\u0639\u062f\u062f\u064b\u0627 \u062d\u0642\u064a\u0642\u064a\u064b\u0627).<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0634\u0643\u0644 \u0645\u0644\u0645\u0648\u0633\u060c \u064a\u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062e\u062a\u0644\u0637 \u0645\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u062c\u0647 \u0644\u0645\u062a\u062c\u0647\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0636\u0631\u0628 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0646\u0627\u0642\u0644 \u062b\u0627\u0644\u062b. \u0627\u0646\u0638\u0631 \u0625\u0644\u0649 \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-20bc6ca73caab65fbe6dafc458258ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.3pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white,shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle   \\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}}) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0645\u0639 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u0641\u0625\u0646 \u062d\u0644 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062e\u062a\u0644\u0637 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0644\u064a\u0633 \u0628\u0627\u0644\u0623\u0645\u0631 \u0627\u0644\u0633\u0647\u0644. \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u0646\u0646\u0635\u062d\u0643 \u0628\u0625\u0644\u0642\u0627\u0621 \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0634\u0631\u062d <a href=\"https:\/\/mathority.org\/ar\/\u0627\u0654\u0645\u062b\u0644\u0629-\u0639\u0644\u0649-\u0627\u0644\u0645\u0646\u062a\u062c\u0627\u062a-\u0627\u0644\u0645\u062e\u062a\u0644\u0637\u0629-\u0644\u062b\u0644\u0627\u062b\u0629-\u0646\u0627\u0642\u0644\u0627\u062a-\u0627\u0654\u0648-\u0627\u0644\u0645\u0646\u062a\u062c\u0627\u062a-\u0627\u0644\u0639\u062f\u062f\u064a\u0629-\u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629\/\">\u0644\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u062e\u062a\u0644\u0637 \u0644\u062b\u0644\u0627\u062b\u0629 \u0646\u0627\u0642\u0644\u0627\u062a<\/a> \u060c \u062d\u064a\u062b \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0648\u0627\u0644\u0645\u0639\u0646\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0647\u0630\u0647.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"tipos-de-vectores\"><\/span> \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0647\u0646\u0627\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u0648\u0644\u0643\u0646 \u0623\u0647\u0645 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u062c\u0628 \u0645\u0639\u0631\u0641\u062a\u0647\u0627 \u0647\u064a:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0645\u062a\u062c\u0647 \u0627\u0644\u0648\u062d\u062f\u0629<\/strong> : \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u062a\u0633\u0627\u0648\u064a \u0648\u062d\u062f\u062a\u0647 1.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062b\u0627\u0628\u062a<\/strong> : \u064a\u062a\u0645 \u062a\u062b\u0628\u064a\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642 \u0623\u0635\u0644 \u0627\u0644\u0645\u062a\u062c\u0647 \u0639\u0644\u0649 \u0646\u0642\u0637\u0629 \u062b\u0627\u0628\u062a\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062d\u0631<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u062d\u0631\u064b\u0627 \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u062a\u0637\u0628\u064a\u0642\u0647\u060c \u0648\u0644\u0643\u0646\u0647 \u0646\u0642\u0637\u0629 \u062d\u0631\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0633\u0627\u0645\u064a\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0645\u062a\u062c\u0647\u0627\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0639\u0644\u0649 \u062e\u0637 \u0648\u0627\u062d\u062f \u0625\u0630\u0627 \u0643\u0627\u0646\u0627 \u064a\u0634\u062a\u0631\u0643\u0627\u0646 \u0641\u064a \u0646\u0641\u0633 \u062e\u0637 \u0627\u0644\u0639\u0645\u0644 (\u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u0642\u0639 \u0641\u064a\u0647 \u0627\u0644\u0645\u062a\u062c\u0647).<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u062a\u0643\u0627\u0641\u0626\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0645\u062a\u0633\u0627\u0648\u064a\u0627\u0646 \u0641\u064a \u062d\u0628\u0648\u0628 \u0627\u0644\u0644\u0642\u0627\u062d \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u062d\u062c\u0645 \u0648\u0646\u0641\u0633 \u0627\u0644\u0645\u0639\u0646\u0649 \u0648\u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 (\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0644\u0647\u0645\u0627 \u0646\u0642\u0627\u0637 \u062a\u0637\u0628\u064a\u0642 \u0645\u062e\u062a\u0644\u0641\u0629).<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629<\/strong> : \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0647\u064a \u0646\u0627\u0642\u0644\u0627\u062a \u0645\u062a\u0633\u0627\u0648\u064a\u0629 \u062a\u0639\u0645\u0644 \u0623\u064a\u0636\u064b\u0627 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u062e\u0637.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0627\u0644\u0645\u062a\u0642\u0627\u0628\u0644\u0627\u0646<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0645\u062a\u0636\u0627\u062f\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u062f\u0627\u0631 \u0648\u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0644\u0643\u0646 \u0641\u064a \u0627\u062a\u062c\u0627\u0647 \u0645\u062e\u062a\u0644\u0641.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0648\u0636\u0639<\/strong> : \u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0648\u0636\u0639 \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u0623\u0635\u0644\u0647 \u0647\u0648 \u0627\u0644\u0646\u0642\u0637\u0629 (0,0) (\u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a).<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u062a\u0646\u0627\u0641\u0633\u0629<\/strong> : \u064a\u062a\u0632\u0627\u0645\u0646 \u0645\u062a\u062c\u0647\u0627\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0639\u0646\u062f\u0645\u0627 \u064a\u0645\u0631 \u062e\u0637 \u0639\u0645\u0644\u0647\u0645\u0627 \u0628\u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629\u060c \u0623\u064a \u0623\u0646\u0647\u0645\u0627 \u064a\u062a\u0642\u0627\u0637\u0639\u0627\u0646.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0645\u062a\u062c\u0647\u0627\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0645\u062a\u0648\u0627\u0632\u064a\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0627\u062a\u062c\u0627\u0647\u0627\u062a\u0647\u0645\u0627.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646 (\u0623\u0648 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646) \u0639\u0646\u062f\u0645\u0627 \u064a\u0634\u0643\u0644 \u0627\u062a\u062c\u0627\u0647\u0647\u0645\u0627 \u0632\u0627\u0648\u064a\u0629 \u0642\u062f\u0631\u0647\u0627 90 \u062f\u0631\u062c\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u062b\u0646\u0627\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636\u060c \u0648\u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0647\u064a \u0648\u062d\u062f\u0648\u064a\u0629 (\u062d\u062c\u0645\u0647\u0627 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0648\u062d\u062f\u0629).<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0629<\/strong> : \u064a\u0643\u0648\u0646 \u0627\u062b\u0646\u0627\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0645\u062a\u062d\u062f\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0645\u0633\u062a\u0648\u0649. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"angulo-entre-dos-vectores\"><\/span> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u062d\u0635\u0648\u0631\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u062d\u062f\u062f\u064a\u0646\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \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-67007d32353dedf96eb6b965b16c5489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.4pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<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-4501274336c637b37c6332eae5c6c229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a59cd4f2581db3318d38a2a77340a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0647\u064a \u0648\u062d\u062f\u0627\u062a \u0645\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-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u0649.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629\u060c \u0633\u062a\u062c\u062f \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a: \u0645\u0627 \u0647\u064a\u060c \u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629\u060c&#8230; \u0645\u0627 \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647\u061f \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0648 \u0642\u0637\u0639\u0629 \u0645\u0648\u062c\u0647\u0629 \u062a\u0646\u062a\u0642\u0644 \u0645\u0646 \u0646\u0642\u0637\u0629 (\u062a\u0633\u0645\u0649 \u0627\u0644\u0623\u0635\u0644) \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 (\u062a\u0633\u0645\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0629). \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0623\u062f\u0646\u0627\u0647\u060c \u064a\u0645\u0643\u0646\u0643 \u0623\u0646 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%85%d8%a7-%d9%87%d9%8a-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%a7%d9%84%d9%81%d9%8a%d8%b2%d9%8a%d8%a7%d8%a1-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87\/\"> <span class=\"screen-reader-text\">\u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a (\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a)\u061f<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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