{"id":213,"date":"2023-07-11T21:43:45","date_gmt":"2023-07-11T21:43:45","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%b6%d8%b1%d8%a8-%d8%ad%d8%a7%d8%b5%d9%84-%d8%b6%d8%b1%d8%a8-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87-%d8%a8%d8%b9%d8%af%d8%af-%d8%ad%d9%82%d9%8a%d9%82%d9%8a\/"},"modified":"2023-07-11T21:43:45","modified_gmt":"2023-07-11T21:43:45","slug":"%d8%b6%d8%b1%d8%a8-%d8%ad%d8%a7%d8%b5%d9%84-%d8%b6%d8%b1%d8%a8-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87-%d8%a8%d8%b9%d8%af%d8%af-%d8%ad%d9%82%d9%8a%d9%82%d9%8a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%b6%d8%b1%d8%a8-%d8%ad%d8%a7%d8%b5%d9%84-%d8%b6%d8%b1%d8%a8-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87-%d8%a8%d8%b9%d8%af%d8%af-%d8%ad%d9%82%d9%8a%d9%82%d9%8a\/","title":{"rendered":"\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a (\u0623\u0648 \u0633\u0644\u0645\u064a) \u0639\u062f\u062f\u064a\u064b\u0627 \u0648\u0631\u0633\u0648\u0645\u064a\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u062a\u0645 \u0623\u064a\u0636\u0627 \u0634\u0631\u062d \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. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-multiplica-un-vector-por-un-numero-real\"><\/span> \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0643 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a\u061f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0639\u062f\u062f (\u0623\u0648 \u0639\u062f\u062f\u064a) \u0639\u062f\u062f\u064a\u064b\u0627\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\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-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\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abb3b5391be9c0e4d871ff45367ca838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\\cdot \\vv{\\text{u}} =(k\\cdot \\text{u}_x \\ , \\ k\\cdot \\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0646\u062a\u064a\u062c\u0629 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0641\u064a \u0639\u062f\u062f \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0638\u0647\u0648\u0631 \u0645\u062a\u062c\u0647 \u062c\u062f\u064a\u062f \u064a\u062a\u0645\u062a\u0639 \u0628\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=;text-align:right;direction:rtl\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"><span style=\"color:#000000;font-weight: normal;\">\u0646\u062a\u064a\u062c\u0629 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629 \u062a\u0646\u062a\u062c \u0645\u062a\u062c\u0647\u064b\u0627 \u062c\u062f\u064a\u062f\u064b\u0627 \u0628\u0646\u0641\u0633 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a.<\/span><\/li>\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u064a\u0643\u0648\u0646 \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062c\u062f\u064a\u062f \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0631\u0642\u0645 \u0645\u0648\u062c\u0628\u064b\u0627.<\/span><\/li>\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0623\u0648 \u0633\u064a\u0643\u0648\u0646 \u0644\u0647 \u0645\u0639\u0646\u0649 \u0645\u0639\u0627\u0643\u0633 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0631\u0642\u0645 \u0633\u0627\u0644\u0628\u0627.<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0646\u0627\u062a\u062c \u064a\u0639\u0627\u062f\u0644 \u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a \u0627\u0644\u0639\u062f\u062f\u064a\u0629.<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \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<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\/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=\"305\" height=\"206\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0646\u0631\u0649 \u0628\u0648\u0636\u0648\u062d \u0623\u0646 \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u062c\u0647 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0627\u062a\u062c \u064a\u0633\u0627\u0648\u064a \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a \u0627\u0644\u0639\u062f\u062f\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\/numero-de-produit-de-multiplication-de-module-par-vecteur.webp\" alt=\"\u0643\u064a\u0641 \u062a\u062a\u0637\u0648\u0631 \u0648\u062d\u062f\u0629 \u0627\u0644\u0636\u0631\u0628 \u0623\u0648 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0631\u0642\u0645 \u0628\u0648\u0627\u0633\u0637\u0629 \u0646\u0627\u0642\u0644\u061f\" class=\"wp-image-290\" width=\"255\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646\u0646\u0627 \u0625\u0630\u0627 \u0636\u0631\u0628\u0646\u0627 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u0623\u0643\u0628\u0631 \u0645\u0646 1\u060c \u0641\u0625\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u0645\u062a\u062c\u0647 \u0628\u0637\u0648\u0644 \u0623\u0643\u0628\u0631 (\u0630\u0648 \u0645\u0639\u0627\u0645\u0644 \u0623\u0643\u0628\u0631). \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0625\u0630\u0627 \u0636\u0631\u0628\u0646\u0627 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u0623\u0642\u0644 \u0645\u0646 1\u060c \u0641\u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0645\u062a\u062c\u0647\u064b\u0627 \u0628\u0637\u0648\u0644 \u0623\u0642\u0635\u0631 (\u0645\u0639\u0627\u0645\u0644 \u0623\u0635\u063a\u0631).<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0644\u0627\u062d\u0638\u0629:<\/strong> \u0644\u0627 \u062a\u062e\u0644\u0637 \u0628\u064a\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0648\u0627\u0644\u0631\u0642\u0645 \u0645\u0639 <a href=\"https:\/\/mathority.org\/ar\/\u062d\u0633\u0627\u0628-\u0627\u0644\u0645\u0646\u062a\u062c-\u0627\u0644\u0642\u064a\u0627\u0633\u064a-\u0628\u064a\u0646-\u0627\u062b\u0646\u064a\u0646-\u0645\u0646-\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a-\u0627\u0654\u0645\u062b\u0644\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0644\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/a> . \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646\u0647\u0645\u0627 \u064a\u062d\u0645\u0644\u0627\u0646 \u0627\u0633\u0645\u064b\u0627 \u0645\u0634\u0627\u0628\u0647\u064b\u0627\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0645\u0627 \u0645\u0641\u0647\u0648\u0645\u0627\u0646 \u0645\u062e\u062a\u0644\u0641\u0627\u0646 \u062a\u0645\u0627\u0645\u064b\u0627. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-del-producto-de-un-vector-por-un-escalar\"><\/span> \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u0646\u062a\u062c \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0631\u0649 \u0645\u062b\u0627\u0644\u064b\u0627 \u0631\u0642\u0645\u064a\u064b\u0627 \u0644\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0639\u062f\u062f:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u0627\u0644\u064a \u0628\u0640 4:<\/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-0a3b02659b94a332ef3cd2cc62769d94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} =(2,-3)\" 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-998ae86a47fde44f6006a0744f03c562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{\\text{u}} =(4 \\cdot 2 \\ , \\ 4 \\cdot (-3)) = \\bm{(8,-12)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"263\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u062a\u060c \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0644\u064a\u0633 \u0645\u0639\u0642\u062f\u064b\u0627 \u0644\u0644\u063a\u0627\u064a\u0629\u060c \u0644\u0623\u0646\u0647 \u0644\u0627 \u064a\u062a\u0639\u064a\u0646 \u0639\u0644\u064a\u0643 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0639\u0645\u0644\u064a\u0627\u062a \u0645\u062a\u062c\u0647\u0629 \u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u064b\u0627\u060c \u0645\u062b\u0644 \u062c\u0645\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0648\u0637\u0631\u062d \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a. \u0625\u0630\u0627 \u0643\u0646\u062a \u0642\u062f \u0641\u0647\u0645\u062a \u0628\u0627\u0644\u0641\u0639\u0644 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629\u060c \u0641\u0646\u0648\u0635\u064a\u0643 \u0628\u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062a\u0627\u0644\u064a \u0648\u0645\u0639\u0631\u0641\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\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\/\">\u062c\u0645\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/a> <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\/\">\u0648\u0637\u0631\u062d \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<\/a> \u060c \u062d\u064a\u062b \u0623\u0646 \u0647\u0630\u0647 \u0639\u0645\u0644\u064a\u0627\u062a \u0623\u0643\u062b\u0631 \u0635\u0639\u0648\u0628\u0629 \u0625\u0644\u0649 \u062d\u062f \u0645\u0627\u060c \u0648\u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0630\u0644\u0643 \u0628\u0643\u062b\u064a\u0631 (\u0641\u0647\u064a \u0623\u0643\u062b\u0631 \u0623\u0647\u0645\u064a\u0629). <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-multiplicacion-de-un-vector-por-un-numero\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0639\u062f\u062f \u0644\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \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>\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062f\u0645\u062c<\/strong> : \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0623\u0643\u062b\u0631 \u0645\u0646 \u0631\u0642\u0645\u060c \u0644\u0627 \u064a\u0647\u0645 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0636\u0631\u0628.<\/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-a7cc3b0e34695b9960f32199046e868e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (k' \\cdot \\vv{\\text{u}}) =(k\\cdot k') \\cdot \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639<\/strong> \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u062c\u0645\u0639 \u0648\u0637\u0631\u062d \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a:<\/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-a8b55a3b25ad66154d6e8bb18fc70da7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}+  \\vv{\\text{v}})=k\\cdot \\vv{\\text{u}} + k\\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" 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-086f60151d160ac3b6d4f5add59434b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}- \\vv{\\text{v}})=k\\cdot \\vv{\\text{u}} - k\\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639<\/strong> \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0625\u0636\u0627\u0641\u0629 \u0627\u0644\u0643\u0645\u064a\u0627\u062a:<\/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-7354955effb7b59f41793537f4517851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(k+k') \\cdot \\vv{\\text{u}} =k\\cdot \\vv{\\text{u}} + k'\\cdot \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f<\/strong> : \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646 \u0623\u064a \u0645\u062a\u062c\u0647 \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a 1 \u064a\u0639\u0637\u064a \u0627\u0644\u0645\u062a\u062c\u0647 \u0646\u0641\u0633\u0647: <\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-154c7987de1e55e762dcf229eae9fd23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot \\vv{\\text{u}} = \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-multiplicacion-de-un-vector-por-un-escalar\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0645\u0642\u062f\u0627\u0631 \u0642\u064a\u0627\u0633\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u062a\u062d\u0644\u064a\u0644\u064a\u0627\u064b \u0646\u062a\u064a\u062c\u0629 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u0627\u0644\u064a \u0628\u0645\u0642\u062f\u0627\u0631 3: <\/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-8b5a56f394f2b178a0175a53e6a55a1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0646\u062a\u062c\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0636\u0631\u0628 \u0643\u0644 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0640 3: <\/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-4e0b8a6167489c27e91bef24f222e3af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot \\vv{a}=(3\\cdot (-2), 3 \\cdot 5) = \\bm{(-6,15)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"250\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u062a\u0627\u0644\u064a \u0641\u064a 6 \u0648\u0627\u0628\u062d\u062b \u0639\u0646 \u0648\u062d\u062f\u062a\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-85db994a57a1325a456909a04efa2e23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(3,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0641\u064a \u0627\u0644\u0639\u062f\u062f\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-7c6c6b2d9291528aff357e7e94daf221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot \\vv{a}=(6\\cdot 3, 6 \\cdot (-4)) = (18,-24)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062a\u0648\u062c\u062f \u0627\u0644\u0622\u0646 \u0637\u0631\u064a\u0642\u062a\u0627\u0646 \u0644\u062d\u0633\u0627\u0628 \u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647. \u0627\u0644\u0623\u0648\u0644 \u0647\u0648 \u0625\u064a\u062c\u0627\u062f \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a\u060c \u062b\u0645 \u0636\u0631\u0628\u0647 \u0641\u064a 6: <\/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-7a7bc760b63c8efa2c36d2d49802000c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =\\sqrt{3^2+(-4)^2} = \\sqrt{25} =5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"229\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32f0e3a2cb32142aa26a1fbb0f3bf9df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot \\lvert \\vv{a} \\rvert =6\\cdot 5 =\\bm{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0647\u064a \u062d\u0633\u0627\u0628 \u062d\u062c\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0641\u064a \u0627\u0644\u0636\u0631\u0628 \u0645\u0628\u0627\u0634\u0631\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-06f0793bfdae917904c47247b9b1f08f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert 6\\cdot \\vv{a} \\rvert =\\sqrt{18^2+(-24)^2} = \\sqrt{900} =\\bm{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"287\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u062d\u064a\u062b \u064a\u0638\u0647\u0631 \u0641\u064a \u0643\u0644\u0627 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u064a\u0646 \u0623\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0644\u0627 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u0627\u0645\u0644.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \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-cf8d63b14f91ee738fe5107ab2a05779_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u062c\u0628\u0631\u064a\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-5557b66d322653674e2266800c73c958_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" 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-a2f511cc4014aae8cf90bef442f30bdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" 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-d09a188710cecb56283c4a2dea7a97e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2} \\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"33\" 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-7c4742e8a37f45e358d2e7740c5aadef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u062d\u062f\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u062a\u062c\u0627\u0647 \u0648\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a\u060c \u0648\u0631\u062a\u0628\u0647\u0627 \u0645\u0646 \u0627\u0644\u0623\u0642\u0635\u0631 \u0625\u0644\u0649 \u0627\u0644\u0623\u0637\u0648\u0644. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627 \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u0636\u0631\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-6b92c621a30ebf15a0628cba3e0f6be5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot \\vv{a}=(2\\cdot 4, 2 \\cdot (-1)) = (8,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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-71e1eb36b88b2ca47d69f0bfe4d1a33b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot \\vv{a}=(-3\\cdot 4, -3 \\cdot (-1)) = (-12,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" 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-d9866b27859b66475a36d182919ec4e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\cdot \\vv{a}=\\left(\\frac{1}{2}\\cdot 4, \\frac{1}{2} \\cdot (-1)\\right) = \\left(2,-\\frac{1}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"277\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6904a22660dc2e21ab3f775e1453535c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{a}=(4\\cdot 4, 4 \\cdot (-1)) = (16,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"250\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u0648\u062c\u0628\u0629 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u062a\u062c\u0627\u0647 \u0648\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a. \u0648\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0645\u0636\u0631\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0644\u0643\u0646 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u0639\u0627\u0643\u0633 \u0644\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0635\u0644\u064a.<\/p>\n<p class=\"has-text-align-center\" style=\";text-align:right;direction:rtl\"> \u0645\u062a\u062c\u0647\u0627\u062a \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\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-50dd29950a1b957a78493d3de5b4bf5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2\\vv{a}, \\ 4\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"50\" 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-9fac7295c812fa36c4fcba97e316b5f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"20\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u062a\u064a \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0644\u0643\u0646 \u0645\u0639\u0646\u0649 \u0645\u062e\u062a\u0644\u0641:<\/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-d1b95a4d066d0dd0da8cdf0373d19c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0648\u0641\u0642\u064b\u0627 \u0644\u0623\u0637\u0648\u0627\u0644\u0647\u0627\u060c \u0623\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644 \u0648\u062d\u062f\u062a\u0647\u0627. \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0630\u0648 \u0627\u0644\u0637\u0648\u0644 \u0627\u0644\u0623\u0637\u0648\u0644 (\u0623\u0648 \u0627\u0644\u0648\u062d\u062f\u0629 \u0627\u0644\u0623\u0643\u0628\u0631) \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u062a\u0645 \u0636\u0631\u0628\u0647 \u0628\u0639\u062f\u062f \u0623\u0643\u0628\u0631 (\u0628\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0642\u0629)\u060c \u0648\u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0623\u0642\u0635\u0631 \u0637\u0648\u0644\u064b\u0627 (\u0623\u0648 \u0623\u0635\u063a\u0631 \u0648\u062d\u062f\u0629) \u0647\u0648 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0630\u064a \u062a\u0645 \u0636\u0631\u0628\u0647 \u0628\u0639\u062f\u062f \u0623\u0635\u063a\u0631 \u0627\u0644\u0631\u0642\u0645 (\u0628\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0642\u0629). \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0623\u0637\u0648\u0627\u0644 \u0647\u0648:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1e7cf58774569c9f128f49948c9fead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} \\displaystyle\\frac{1}{2}\\vv{a}\\end{vmatrix} <\\lvert 2\\vv{a}\\rvert < \\lvert -3\\vv{a}\\rvert < \\lvert 4\\vv{a}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"199\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u0637\u0648\u0644 \u0623\u0648 \u0627\u0644\u0645\u0642\u064a\u0627\u0633 \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0645\u0636\u0631\u0648\u0628\u060c \u0644\u0623\u0646 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u062c\u0647 \u0644\u0627 \u064a\u0639\u062f\u0644 \u0645\u0639\u0627\u0645\u0644\u0647.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0645\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-740cd5f2540cb57342f82c58e1076cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a} =(7,-2) \\qquad \\vv{b} =(-3,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"205\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0639\u0645\u0644\u064a\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-5abd316200fbcf062072dfdf51266cda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\vv{a} - 3 \\vv{b}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\u062d\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0628\u0627\u0644\u0623\u0631\u0642\u0627\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-08a07c35741b9e7427990abb5bb89ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot \\vv{a} - 3 \\cdot \\vv{b}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-5fa31543d7c2a129c47b030cfa5fc4e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot (7,-2) - 3 \\cdot(-3,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7624e801962ac397ca316243c4e3420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(14,-4) - (-9,15)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062b\u0645 \u0646\u0637\u0631\u062d \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-72660b240eab9459d0b0aefb1d10d728_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(14-(-9),-4-15)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" 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-fe8b5f018f4a24a925bfce0c2c997dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(23,-19)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0645 \u0628\u0625\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0627\u062a \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0648\u0631\u0633\u0645 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0628\u064a\u0627\u0646\u064a\u064b\u0627: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1c2fa6e2c114b3bbce76ca987020ad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" 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-1adddd551d57bc95b951c6573080090a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot (-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" 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-33be3689306562b8a4ae74d0970fc1f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot (2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" 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-bd3d3bba47ccc84d7616e38ca863b22d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{2}\\cdot (-2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"76\" 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-8fe6e18de5ed93f74fa207a3f9ecc2c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -\\frac{1}{2}\\cdot (8,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"77\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0641\u064a \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0627\u0644\u062d\u0642\u064a\u0642\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-6846258bc5f69aaea3f86991095d3199_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (1,2) = (2\\cdot 1,2\\cdot 2)=\\bm{(2,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"230\" 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-605e263cab7e34f01290372f0e2666c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot (-1,1) = (-3\\cdot (-1),-3\\cdot 1)=\\bm{(3,-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"325\" 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-b8b4cf7b606673d72ae9cdd0004f0757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot (2,1) = (4\\cdot 2,4\\cdot 1)=\\bm{(8,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"230\" 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-51454cc5c3239bb4552918b1a693b499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{2}\\cdot (-2,4)= \\left(\\frac{3}{2}\\cdot (-2), \\frac{3}{2}\\cdot 4 \\right) = \\bm{(-3,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"307\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8fbbfff835499e861d11de5da6714d10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -\\frac{1}{2}\\cdot (8,6)= \\left(-\\frac{1}{2}\\cdot 8, -\\frac{1}{2}\\cdot 6 \\right) = \\bm{(-4,-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"322\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0628\u0645\u062c\u0631\u062f \u0642\u064a\u0627\u0645\u0646\u0627 \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0645\u062b\u0644\u0647\u0627 \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a: <\/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\/exercices-et-problemes-resolus-de-multiplication-dun-vecteur-par-un-nombre.webp\" alt=\"\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0641\u064a \u0639\u062f\u062f\" class=\"wp-image-327\" width=\"469\" height=\"370\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a (\u0623\u0648 \u0633\u0644\u0645\u064a) \u0639\u062f\u062f\u064a\u064b\u0627 \u0648\u0631\u0633\u0648\u0645\u064a\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u062a\u0645 \u0623\u064a\u0636\u0627 \u0634\u0631\u062d \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. \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0643 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a\u061f \u0644\u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0639\u062f\u062f (\u0623\u0648 \u0639\u062f\u062f\u064a) \u0639\u062f\u062f\u064a\u064b\u0627\u060c \u064a\u062c\u0628 \u0636\u0631\u0628 \u0643\u0644 \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u0643\u0648\u0646\u0627\u062a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%b6%d8%b1%d8%a8-%d8%ad%d8%a7%d8%b5%d9%84-%d8%b6%d8%b1%d8%a8-%d8%a7%d9%84%d9%85%d8%aa%d8%ac%d9%87-%d8%a8%d8%b9%d8%af%d8%af-%d8%ad%d9%82%d9%8a%d9%82%d9%8a\/\"> <span class=\"screen-reader-text\">\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[21],"tags":[],"class_list":["post-213","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0631\u0642\u0645 - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ar\/\u0636\u0631\u0628-\u062d\u0627\u0635\u0644-\u0636\u0631\u0628-\u0627\u0644\u0645\u062a\u062c\u0647-\u0628\u0639\u062f\u062f-\u062d\u0642\u064a\u0642\u064a\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0631\u0642\u0645 - Mathority\" \/>\n<meta property=\"og:description\" content=\"\u062a\u0634\u0631\u062d \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a (\u0623\u0648 \u0633\u0644\u0645\u064a) \u0639\u062f\u062f\u064a\u064b\u0627 \u0648\u0631\u0633\u0648\u0645\u064a\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0628\u0643\u0645\u064a\u0629 \u0642\u064a\u0627\u0633\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u062a\u0645 \u0623\u064a\u0636\u0627 \u0634\u0631\u062d \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. \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0643 \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a\u061f \u0644\u062d\u0633\u0627\u0628 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u062c\u0647 \u0648\u0639\u062f\u062f (\u0623\u0648 \u0639\u062f\u062f\u064a) \u0639\u062f\u062f\u064a\u064b\u0627\u060c \u064a\u062c\u0628 \u0636\u0631\u0628 \u0643\u0644 \u0645\u0643\u0648\u0646 \u0645\u0646 \u0645\u0643\u0648\u0646\u0627\u062a &hellip; \u0636\u0631\u0628 \u0627\u0644\u0645\u062a\u062c\u0647 \u0628\u0639\u062f\u062f \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ar\/\u0636\u0631\u0628-\u062d\u0627\u0635\u0644-\u0636\u0631\u0628-\u0627\u0644\u0645\u062a\u062c\u0647-\u0628\u0639\u062f\u062f-\u062d\u0642\u064a\u0642\u064a\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-11T21:43:45+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4b2f8c9cdb09377a66fbce8392c30ec_l3.png\" 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