{"id":72,"date":"2023-09-16T13:06:27","date_gmt":"2023-09-16T13:06:27","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%83%d9%8a%d9%81%d9%8a%d8%a9-%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d9%85%d8%aa%d8%ac%d9%87%d9%8a%d9%86-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%aa%d9%85\/"},"modified":"2023-09-16T13:06:27","modified_gmt":"2023-09-16T13:06:27","slug":"%d9%83%d9%8a%d9%81%d9%8a%d8%a9-%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d9%85%d8%aa%d8%ac%d9%87%d9%8a%d9%86-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%aa%d9%85","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%83%d9%8a%d9%81%d9%8a%d8%a9-%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d9%85%d8%aa%d8%ac%d9%87%d9%8a%d9%86-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%aa%d9%85\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u0643\u062a\u0634\u0641 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0648\u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-dos-vectores\"><\/span> \u0635\u064a\u063a\u0629 \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<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-entre-deux-vecteurs-et-produit-scalaire.webp\" alt=\"\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 \u0644\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\u064a\" class=\"wp-image-583\" width=\"187\" height=\"190\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u062a\u0630\u0643\u0631\u0646\u0627 <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\/\">\u062a\u0639\u0631\u064a\u0641 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a<\/a> \u0641\u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\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-66d255d6dd1b74f0a5cd6a209c2a9505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}} \\cdot \\vv{\\text{v}} = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert \\cdot \\cos(\\alpha )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u064a \u0633\u062a\u0633\u0627\u0639\u062f\u0646\u0627 \u0641\u064a \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u0646 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u0646 \u064a\u0633\u0627\u0648\u064a \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u0639\u0627\u0645\u0644\u064a \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646.<\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0635\u064a\u063a\u0629 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u0646 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\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\/formule-dangle-entre-deux-vecteurs.webp\" alt=\"\u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646\" class=\"wp-image-587\" width=\"270\" height=\"128\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u0634\u0643\u0644\u0647\u0627 \u0645\u062a\u062c\u0647\u0627\u0646\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u062a\u0639\u0631\u0641 \u0643\u064a\u0641\u064a\u0629 <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\/\">\u062d\u0633\u0627\u0628 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062c\u0647<\/a> . \u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u0635\u064a\u063a\u0629 \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u0644\u0648\u062d\u062f\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u0644\u0630\u0627 \u0625\u0630\u0627 \u0644\u0645 \u062a\u0643\u0646 \u0642\u062f \u0623\u062a\u0642\u0646\u062a \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0647\u0630\u0647 \u0628\u0639\u062f\u060c \u0641\u0646\u0648\u0635\u064a\u0643 \u0628\u0625\u0644\u0642\u0627\u0621 \u0646\u0638\u0631\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0639\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 (\u0641\u064a R2) \u0648\u0627\u0644\u0645\u0633\u0627\u062d\u0629 (\u0641\u064a R3). \u0648\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0628\u0627\u0644\u062a\u0628\u0627\u062f\u0644 \u0645\u0639 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0639\u0646\u0635\u0631\u064a\u0646 \u0623\u0648 \u062b\u0644\u0627\u062b\u0629 \u0645\u0643\u0648\u0646\u0627\u062a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 <strong>\u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646<\/strong> (\u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0627\u062a\u062c\u0627\u0647) \u0647\u064a 0 \u062f\u0631\u062c\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 <strong>\u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646<\/strong> (\u0623\u0648 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646) \u0647\u064a 90 \u062f\u0631\u062c\u0629. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-el-angulo-entre-dos-vectores\"><\/span> \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u0625\u064a\u062c\u0627\u062f \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\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0648\u0641 \u0646\u062d\u0633\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0627\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-9f9ae15324c67998fbf5bb3a1a23a39b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,-1) \\qquad \\vv{\\text{v}} = (2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u0627\u064b \u062d\u0633\u0627\u0628 \u0648\u062d\u062f\u0629 \u0643\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-407fe81f99d6f328024431ce1264a262_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{4^2+(-1)^2}= \\sqrt{17}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"198\" 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-6f8f801f8b137ed446af80104eaeba37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{v}} \\rvert = \\sqrt{2^2+5^2}= \\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"170\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0622\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u062d\u0633\u0627\u0628 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b1f1619914a14d6cf7117760d651a0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}=\\cfrac{ 4\\cdot 2 + (-1)\\cdot 5}{\\sqrt{17}\\cdot \\sqrt{29}} = \\cfrac{3}{\\sqrt{493}} = 0,14\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u0645\u0639\u0643\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26875d19d098689f9f1829db2a0a5b7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos^{-1}(0,14) = \\bm{81,95\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0634\u0643\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0632\u0627\u0648\u064a\u0629 \u0642\u062f\u0631\u0647\u0627 81.95 \u062f\u0631\u062c\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-angulos-entre-vectores\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a<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 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u062d\u0635\u0648\u0631\u0629 \u0628\u064a\u0646 \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-499126756373eb2239008634feec46c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}}=(5,3) \\qquad  \\vv{\\text{v}} =(1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"180\" 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\"> \u0623\u0648\u0644\u064b\u0627\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062d\u0633\u0627\u0628 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ec0bd408f2cb730372b129c07447bb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{5^2+3^2}= \\sqrt{34}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"170\" 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-1f75602deaa00b7d68322e42455d4954_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{v}} \\rvert = \\sqrt{ 1^2+2^2}= \\sqrt{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"161\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u062d\u0633\u0627\u0628 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a:<\/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-26d67b7514a805a0fd3ad15191fbd1c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}=\\cfrac{ 5\\cdot 1 + 3\\cdot 2}{\\sqrt{34}\\cdot \\sqrt{5}} = \\cfrac{11}{\\sqrt{170}} = 0,84\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"360\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062c\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u0645\u0639\u0643\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c08fd9d0bf6afbf2cc5b22809df64d3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos^{-1}(0,84) = \\bm{32,47\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"158\" 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\"> \u062d\u062f\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0628\u064a\u0646 \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-608b8fbebe6a76c94f7260810ae1dcdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}}=(-2,-7) \\qquad  \\vv{\\text{v}} =(-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" 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\"> \u0623\u0648\u0644\u064b\u0627\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0648\u062d\u062f\u0627\u062a \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-751a8c816f55c14f3c48b2c863c3efa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ (-2)^2+(-7)^2}= \\sqrt{53}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"225\" 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-c8a9191c8cc87d5eeb9ba2adef3860f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{v}} \\rvert = \\sqrt{ (-1)^2+5^2}= \\sqrt{26}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u064a\u0647\u0627 \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-bbea7ef49f40b0d70811175b255fc3d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}=\\cfrac{ (-2)\\cdot (-1) + (-7)\\cdot 5}{\\sqrt{53}\\cdot \\sqrt{26}} = \\cfrac{-33}{\\sqrt{1378}} = -0,89\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"465\" style=\"vertical-align: -17px;\"><\/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\u0645\u0643\u0646\u0646\u0627 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u062c\u0631\u0627\u0621 \u0645\u0639\u0643\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db9c37ff21d0c5d933f0600eb634035f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos^{-1}(-0,89) = \\bm{152,74\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0642\u064a\u0645\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u062a\u0639\u0627\u0645\u062f\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-0c3383b73b240784dc6b044cc5a3b10a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}}=(6,3) \\qquad  \\vv{\\text{v}} =(-4,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"195\" 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\"> \u064a\u0634\u0643\u0644 \u0645\u062a\u062c\u0647\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u0627\u0646 \u0632\u0627\u0648\u064a\u0629 \u0642\u062f\u0631\u0647\u0627 90 \u062f\u0631\u062c\u0629. \u062d\u062a\u0649 \u0627\u0644\u0622\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-e83a6b694c8dfa0975854f1bffec44de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(90\u00ba) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"133\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ef11c2ecbf7bc8dff4217a761960387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0=\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"86\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u0642\u0627\u0645 \u0627\u0644\u0643\u0633\u0631 \u064a\u0642\u0633\u0645 \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0645\u0646 \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u062d\u062a\u0649 \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u0636\u0631\u0628\u0647 \u0641\u064a \u0627\u0644\u0637\u0631\u0641 \u0627\u0644\u0622\u062e\u0631: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-797dd0ce47130f959c984510894f08b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert  =\\vv{\\text{u}} \\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" 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-b58e54d3d5fa6e123ca5e27a27d77ad1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0  =\\vv{\\text{u}} \\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\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-ee1d711c5614be091814b91a3ad3affa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(6,3) \\cdot (-4,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" 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-e2cd46b62546f556478c5a3b070dd0f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =6 \\cdot (-4) + 3\\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" 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-a4cc0480b00da3aba9adb1d3aaf37325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =-24 +3k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627\u064b \u0646\u0643\u0634\u0641 \u0627\u0644\u0644\u063a\u0632: <\/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-7c13e237f419b6189e700d3b375233c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -3k =-24\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"87\" 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-28ec14747b40a0cd14929b157215c4e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k =\\cfrac{-24}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" 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-54d31d581504a9c867c5f29e53acd788_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =8}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/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 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u064a \u064a\u062c\u0628 \u0623\u0646 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u064a\u0647\u0627 \u0627\u0644\u062b\u0648\u0627\u0628\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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" 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-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u062a\u0639\u0627\u0645\u062f\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0623\u0646\u0647\u0627 \u0635\u062d\u064a\u062d\u0629 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f1e9bd6329419b155da0ff40b9d61e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =10.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"63\" 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-b32214ac021a1b48b4643fea940062ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{u}}=(-6,a) \\qquad  \\vv{\\text{v}} =(b,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" 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\"> \u0633\u0646\u0633\u062a\u062e\u062f\u0645 \u0623\u0648\u0644\u064b\u0627 \u0634\u0631\u0637 \u0627\u0644\u0645\u0642\u064a\u0627\u0633 \u0644\u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fad90838c7fa310bdbea2364787ced6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-c247d22a0918c32059ba3ddaaff4fbfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =10\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"59\" 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-d28001c5a9398f2653cdda9fc6ca3070_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{(-6)^2+a^2}=10\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"141\" 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-43d07a907289c2425d41ef63f6ff1acd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{36+a^2}=10\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0631\u0641\u0639 \u0637\u0631\u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\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-82bc99f0d181db4e2499a41633bafc8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\sqrt{36+a^2}\\right)^2=10^2\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"146\" style=\"vertical-align: -11px;\"><\/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-b950dcac0bf08532d7e6f5d41b7de602_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"36+a^2=100\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0643\u0634\u0641 \u0627\u0644\u0644\u063a\u0632: <\/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-0d2957cd064f117478d48077c1d6a7be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2=100 -36\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"107\" 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-bbc56fe6fb2923832590bd589be0c593_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2=64\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" 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-16b2f840c377014039359be948ab832b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=\\sqrt{64}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7897d0ec97cc23b3a386de3efb8e2466_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=8}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0642\u064a\u0645\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u060c \u0623\u0648\u062c\u062f \u0642\u064a\u0645\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646\u060c \u062d\u064a\u062b \u0623\u0646 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u062a\u062e\u0628\u0631\u0646\u0627 \u0623\u0646\u0647\u0645\u0627 \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646\u0627 \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646\u060c \u0623\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644\u0647\u0645\u0627\u060c \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646\u0627 90 \u062f\u0631\u062c\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-e83a6b694c8dfa0975854f1bffec44de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(90\u00ba) =\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"133\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ef11c2ecbf7bc8dff4217a761960387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0=\\cfrac{\\vv{\\text{u}} \\cdot \\vv{\\text{v}}}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"86\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u0642\u0627\u0645 \u0627\u0644\u0643\u0633\u0631 \u064a\u0642\u0633\u0645 \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0645\u0646 \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u062d\u062a\u0649 \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u0636\u0631\u0628\u0647 \u0641\u064a \u0627\u0644\u0637\u0631\u0641 \u0627\u0644\u0622\u062e\u0631: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-797dd0ce47130f959c984510894f08b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert  =\\vv{\\text{u}} \\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" 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-b58e54d3d5fa6e123ca5e27a27d77ad1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0  =\\vv{\\text{u}} \\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u062f\u0639\u0648\u0646\u0627 \u0646\u062d\u0627\u0648\u0644 \u062d\u0644 \u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0646\u0642\u0637\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-cc125de9cd9b958bb85b7ffb79ef91ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(-6,8) \\cdot (b,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" 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-67a24872ace77b1c8cbc512d361d9866_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =-6 \\cdot b +8\\cdot 3\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"128\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dfbbe49209a7e767517fab13634eaf8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =-6b +24\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"102\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627\u064b \u0646\u0643\u0634\u0641 \u0627\u0644\u0644\u063a\u0632: <\/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-b73000a4e9d07e053e2b45eb4522a7aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 6b =24\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" 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-33bb24f252697112b44e30bc9f9240ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle b =\\cfrac{24}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"51\" 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-13d0b4768ea510b5e1b989f4eeb9deb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{b =4}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\"><\/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\"> \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0648\u0627\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-28575fb8fa361427b255d8744e982cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha , \\beta\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"30\" 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-4de02fc502ed5dbd15f371728ea270a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\gamma\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0648\u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u062a\u0627\u0644\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\/exercice-angle-resolu-entre-vecteurs-produit-scalaire.webp\" alt=\"\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0645\u0633\u0627\u0626\u0644 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0642\u064a\u0627\u0633\u064a \u0644\u0645\u062a\u062c\u0647\u064a\u0646\" class=\"wp-image-560\" width=\"290\" height=\"226\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\"> \u0627\u0644\u0631\u0621\u0648\u0633 \u0627\u0644\u062a\u064a \u064a\u062a\u0643\u0648\u0646 \u0645\u0646\u0647\u0627 \u0627\u0644\u0645\u062b\u0644\u062b \u0647\u064a \u0627\u0644\u0646\u0642\u0627\u0637 \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-75a4919fae29190e3effdeedcec8eb6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1) \\qquad B(4,4) \\qquad C(6,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"230\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u0629 \u0644\u0644\u0645\u062b\u0644\u062b\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0645\u062a\u062c\u0647\u0627\u062a \u0643\u0644 \u062c\u0627\u0646\u0628 \u0645\u0646 \u0623\u0636\u0644\u0627\u0639\u0647 \u062b\u0645 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0634\u0643\u0644\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0632\u0627\u0648\u064a\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0646\u062d\u0633\u0628 \u0645\u062a\u062c\u0647\u0627\u062a \u062c\u0648\u0627\u0646\u0628\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-6a9da14fa9cc4e50b06bdfa76801b083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (4,4)-(2,1)= (2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"287\" 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-8e4e2e72bee87bba3e7657a53935e660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (6,2)-(2,1)= (4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0648\u062c\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0636\u0631\u0628 \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-7b6aad49b300d421fc3bb486f051294c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{AB} \\rvert = \\sqrt{2^2+3^2} = \\sqrt{13}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6657897e68d6b68f79277c89abe6868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{AC} \\rvert = \\sqrt{4^2+1^2} = \\sqrt{17}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a966db5753cbb53c424c0f962fb27102_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\vv{AB} \\cdot \\vv{AC}}{\\lvert \\vv{AB} \\rvert \\cdot \\lvert \\vv{AC} \\rvert}=\\cfrac{ 2\\cdot 4 + 3\\cdot 1}{\\sqrt{13}\\cdot \\sqrt{17}} = \\cfrac{11}{\\sqrt{221}} =0,74\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"396\" 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-9fac783dc0113263dfb5c31b58231fae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\alpha = 42,27\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"79\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0643\u0631\u0631 \u0646\u0641\u0633 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea160d5901518098e691e051e6efa4a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\beta:\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-398c0b2dc840abfc63700a084e9e2956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} = C - B = (6,2)-(4,4)= (2,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"302\" 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-b7825d9e3b0ceee57e7ecd470e52a242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{BC} \\rvert = \\sqrt{2^2+(-2)^2} = \\sqrt{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"207\" 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-e0e73fd58d6a5b487af9f971fdcdc97f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\beta) =\\cfrac{\\vv{AB} \\cdot \\vv{BC}}{\\lvert \\vv{AB} \\rvert \\cdot \\lvert \\vv{BC} \\rvert}=\\cfrac{ 2\\cdot 2 + 3\\cdot (-2)}{\\sqrt{13}\\cdot \\sqrt{8}} = \\cfrac{-2}{\\sqrt{104}} =-0,20\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"437\" 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-1b2f148d28b9679b8267886497e16518_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\beta = 101,31\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0623\u062e\u064a\u0631\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0643\u0631\u0627\u0631 \u0646\u0641\u0633 \u0627\u0644\u0625\u062c\u0631\u0627\u0621. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0632\u0648\u0627\u064a\u0627 \u0627\u0644\u0645\u062b\u0644\u062b 180 \u062f\u0631\u062c\u0629\u060c \u0644\u0630\u0644\u0643: <\/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-662cae07e8d96d1164dad2b0358302fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\gamma = 180 -42,27-101,31 = \\bm{36,42\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"266\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u0643\u062a\u0634\u0641 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0648\u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0635\u064a\u063a\u0629 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646 \u0625\u0630\u0627 \u062a\u0630\u0643\u0631\u0646\u0627 \u062a\u0639\u0631\u064a\u0641 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u064a \u0641\u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: \u0648\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u064a \u0633\u062a\u0633\u0627\u0639\u062f\u0646\u0627 \u0641\u064a \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u062a\u064a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%83%d9%8a%d9%81%d9%8a%d8%a9-%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-%d8%a8%d9%8a%d9%86-%d9%85%d8%aa%d8%ac%d9%87%d9%8a%d9%86-%d8%a3%d9%85%d8%ab%d9%84%d8%a9-%d8%aa%d9%85\/\"> <span class=\"screen-reader-text\">\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u062c\u0647\u064a\u0646<\/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-72","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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