{"id":213,"date":"2023-07-11T20:48:25","date_gmt":"2023-07-11T20:48:25","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bc%d0%be%d0%b4%d1%83%d0%bb%d1%8c-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b8-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d1%8b-%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%80%d0%b5%d1%88\/"},"modified":"2023-07-11T20:48:25","modified_gmt":"2023-07-11T20:48:25","slug":"%d0%bc%d0%be%d0%b4%d1%83%d0%bb%d1%8c-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b8-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d1%8b-%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%80%d0%b5%d1%88","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bc%d0%be%d0%b4%d1%83%d0%bb%d1%8c-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b8-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d1%8b-%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%80%d0%b5%d1%88\/","title":{"rendered":"\u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0435\u0435 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043c\u043e\u0434\u0443\u043b\u044c \u043f\u043e \u0434\u0432\u0443\u043c \u0442\u043e\u0447\u043a\u0430\u043c: \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u043e \u0438 \u043a\u043e\u043d\u0435\u0446. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044e \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043c\u043e\u0434\u0443\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0412\u044b \u0434\u0430\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-modulo-de-un-vector\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0412\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u043e\u043c \u0438 \u043a\u043e\u043d\u0446\u043e\u043c. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 <strong>\u0434\u043b\u0438\u043d\u0435<\/strong> \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/module-dune-longueur-de-vecteur.webp\" alt=\"\u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0434\u043b\u0438\u043d\u044b\" class=\"wp-image-353\" width=\"182\" height=\"179\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0432\u044b\u0448\u0435, \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043f\u043e\u043b\u043e\u0441\u043e\u0439 \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7513a2086faba37053531b9addea2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{AB}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441 <strong>\u043d\u043e\u0440\u043c\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> , \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u0434\u0435\u0442\u044c, \u0447\u0442\u043e \u043e\u043d \u0437\u0430\u043f\u0438\u0441\u0430\u043d \u0442\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c. \u0412\u043e\u0442 \u043f\u043e\u0447\u0435\u043c\u0443 \u0435\u0441\u0442\u044c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0447\u0435\u0440\u0442\u0430\u043c\u0438 \u0441 \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdcec36c9625381e65a49270cd8a2331_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\lvert \\vv{AB}\\rvert\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-modulo-de-un-vector\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u043e\u0434\u0443\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\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;\">\n<p style=\"text-align:left\"> \u0427\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c <strong>\u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430,<\/strong> \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c (\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439) \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u0441\u0443\u043c\u043c\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0435\u0433\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0445. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440:<\/p>\n<\/p>\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:left\"> \u0415\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f63fa0a6f4110553705d4e3d6cf23692_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{u}} \\rvert = \\sqrt{ \\text{u}_x^2+\\text{u}_y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"117\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<\/div>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043c\u044b \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e1f083b8e9df80dc493a280f5c20cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c93cbb567f755c6f6f5ed9ddd8fce245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert =\\sqrt{4^2+3^2} = \\sqrt{16+9}=\\sqrt{25} = \\bm{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"285\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-el-modulo-de-un-vector-con-las-coordenadas-de-su-origen-y-su-extremo\"><\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u0430 \u0438 \u043a\u043e\u043d\u0446\u0430.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0437\u043d\u0430\u0435\u043c \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b, \u043d\u043e \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e \u0431\u044b, \u0435\u0441\u043b\u0438 \u0431\u044b \u043c\u044b \u0437\u043d\u0430\u043b\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0447\u043a\u0438, \u0433\u0434\u0435 \u043e\u043d \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u0438 \u0433\u0434\u0435 \u0437\u0430\u043a\u0430\u043d\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f?<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u0430 \u0438 \u043a\u043e\u043d\u0446\u0430, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0432\u0430 \u0448\u0430\u0433\u0430:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0435\u0441\u0442\u044c \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u043c\u0438\u043d\u0443\u0441 \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u0410 \u0437\u0430\u0442\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043c\u043e\u0434\u0443\u043b\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435.<\/span><\/li>\n<\/ol>\n<p> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f, \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n<ul>\n<li> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043d\u0430\u0447\u0430\u043b\u043e\u043c \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0430\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a16d799fdc0fa3c371c35ba5f0f3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0443\u043d\u043a\u0442\u0430<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a3a744084783890d8d12db98e82e348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(-1,4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u044b\u0447\u0438\u0442\u0430\u0435\u043c \u0435\u0433\u043e \u043a\u043e\u043d\u0435\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043c\u0438\u043d\u0443\u0441 \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2837e9a238c2d7143e91f36f1bdc953d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A=(-1,4)-(2,1)=(-3,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0417\u043d\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32da93798b33cfd623c145783850b8b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\vv{AB} \\end{vmatrix} =\\sqrt{(-3)^2+3^2} = \\sqrt{9+9}=\\sqrt{18}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"295\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0410 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c \u043a\u043e\u0440\u043d\u0435\u043c, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d \u043d\u0435\u0442\u043e\u0447\u043d\u044b\u0439. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-las-componentes-de-un-vector-a-partir-de-su-modulo\"><\/span> \u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044e <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> \u041c\u044b \u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0430\u043a \u0438\u0437\u0432\u043b\u0435\u0447\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0438\u0437 \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432, \u043d\u043e \u044d\u0442\u043e\u0442 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u044c \u0432\u0441\u043f\u044f\u0442\u044c. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0447\u0435\u0440\u0435\u0437 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c.<\/p>\n<p> \u041f\u0440\u043e\u0446\u0435\u0441\u0441 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u043c \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c<\/strong> . \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0440\u0430\u0437\u043b\u043e\u0436\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440, \u043d\u0430\u043c, \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u043d\u0443\u0436\u043d\u0430 \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0438 \u0443\u0433\u043e\u043b, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u043d \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0441 \u043e\u0441\u044c\u044e \u0430\u0431\u0441\u0446\u0438\u0441\u0441 (\u043e\u0441\u044c X).<\/p>\n<p> \u0422\u0430\u043a \u0447\u0442\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 X \u0438 Y \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/decomposition-dun-vecteur-dans-matab.webp\" alt=\"\u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0432 Matlab\" class=\"wp-image-388\" width=\"390\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0430 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0438, \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0441\u043e \u0441\u0432\u043e\u0438\u043c\u0438 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438.<\/p>\n<p> \u041d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u0432 \u043e\u0442\u043b\u0438\u0447\u0438\u0435 \u043e\u0442 \u043c\u043e\u0434\u0443\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0441\u0438\u043d\u0443\u0441 \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043c\u043e\u0433\u0443\u0442 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0440\u0435\u0448\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0438 \u0443\u0433\u043e\u043b \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0441 \u043e\u0441\u044c\u044e OX \u0440\u0430\u0432\u043d\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3899abb56397b041d612a1fb9d33a70a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert = 10 \\qquad \\alpha = 60\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u043c\u043e\u0434\u0443\u043b\u044e, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0443\u0433\u043b\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3b237fcbcb6df7294c9b2dd5d7f06cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_x= \\lvert \\vv{\\text{u}}\\rvert \\cdot \\text{cos}(60\u00ba)= 10 \\cdot 0,5 = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0410 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u043c\u043e\u0434\u0443\u043b\u044f \u043d\u0430 \u0441\u0438\u043d\u0443\u0441 \u0443\u0433\u043b\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2f9805cff94727a43f3bf53e78e9133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_y= \\lvert \\vv{\\text{u}}\\rvert \\cdot \\text{sen}(60\u00ba)= 10 \\cdot 0,87 = 8,7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"268\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8137f59704bc3ee0eabf752d669ce25d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{ = (5 \\ ,\\ 8,7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-modulo-de-un-vector\"><\/span> \u041c\u043e\u0434\u0443\u043b\u044c\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u043e\u0434\u0443\u043b\u044c \u2014 \u044d\u0442\u043e \u0442\u0438\u043f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438:<\/p>\n<ul>\n<li> \u0412\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <strong>\u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439<\/strong> , \u043e\u043d\u0430 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u0438\u043b\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-923d73a359ab40f1ffaba643bff0ca98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert \\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0441 \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439, &#8212; \u044d\u0442\u043e \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u0442.\u0435. \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3fbfff66ff910ebae6196cf59b4251eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (0,0) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0412\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e (\u0438\u043b\u0438 \u0441\u043a\u0430\u043b\u044f\u0440) \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u043a\u0430\u043b\u044f\u0440\u0430 \u043d\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0438\u043c\u0435\u0435\u0442 \u043c\u0435\u0441\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c814e6a42f23a1c1ab2c413261fa3d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert k \\cdot \\vv{\\text{u}} \\rvert = \\lvert k  \\rvert \\cdot \\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0422\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e<\/strong> \u043f\u0440\u043e\u0432\u0435\u0440\u0435\u043d\u043e: \u043c\u043e\u0434\u0443\u043b\u044c \u0441\u0443\u043c\u043c\u044b \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043c\u0435\u043d\u044c\u0448\u0435 \u0438\u043b\u0438 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 \u0438\u0445 \u043c\u043e\u0434\u0443\u043b\u0435\u0439 \u043f\u043e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63e1eae823666827bce2c51133a8a49b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}+\\vv{\\text{v}} \\rvert \\leq \\lvert\\vv{\\text{u}} \\rvert+\\lvert\\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0441\u0443\u043c\u043c\u044b \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441\u043e \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a16809d6f89f2053f5c732a7acd486ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}+\\vv{\\text{v}} \\rvert = \\sqrt{\\lvert \\vv{\\text{u}} \\rvert ^2+\\lvert \\vv{\\text{v}} \\rvert ^2 +2\\cdot \\vv{\\text{u}}\\cdot \\vv{\\text{v}} \\vphantom{\\sqrt{x^2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"242\" style=\"vertical-align: -9px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"vector-unitario\"><\/span> \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 <strong>\u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c<\/strong> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440, \u043c\u043e\u0434\u0443\u043b\u044c \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0440\u0430\u0432\u0435\u043d \u0435\u0434\u0438\u043d\u0438\u0446\u0435.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d377140c532b698d7cdb3b180f2b7e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u043b\u0438\u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u0435\u0434\u0438\u043d\u0438\u0446\u0435.<\/p>\n<p> \u041c\u043e\u0436\u0435\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u043e\u0447\u0435\u043d\u044c \u0442\u0440\u0443\u0434\u043d\u044b\u043c, \u0447\u0442\u043e\u0431\u044b \u0432\u0435\u043a\u0442\u043e\u0440 \u0438\u043c\u0435\u043b \u043c\u043e\u0434\u0443\u043b\u044c, \u0440\u0430\u0432\u043d\u044b\u0439 \u0440\u043e\u0432\u043d\u043e 1, \u043d\u043e \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043d\u0430\u0439\u0442\u0438 \u044d\u0442\u043e\u0442 \u0442\u0438\u043f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043b\u0435\u0433\u043a\u043e: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043b\u044e\u0431\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u0440\u043e\u0441\u0442\u043e \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u0435 \u0435\u0433\u043e \u043d\u0430 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b8ce39ff18883208f914f48d4463051_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_u = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"64\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0417\u043e\u043b\u043e\u0442\u043e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62e58ce540d042ffd138cfec23ebac58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_u\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> &#8212; \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d6a20023310ef9d6c49931c265af1ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}},\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a59cd4f2581db3318d38a2a77340a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0432\u0430\u0448 \u043c\u043e\u0434\u0443\u043b\u044c.<\/p>\n<\/div>\n<p> \u0415\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0432\u0435\u0440\u0441\u043e\u0440\u043e\u043c \u0438\u043b\u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c.<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0438\u043c\u0435\u0435\u0442 \u0442\u043e \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435, \u0447\u0442\u043e \u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06fc528ca9d541ea032c50af916549a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u043e\u0440\u043c\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440, \u043d\u0430\u043c \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86ef7a2aa2d0201e764e4868b473b3e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert=\\sqrt{1^2+(-1)^2} = \\sqrt{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"188\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-668d60d54811f2fd2be96dd0180563ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{\\text{v}}_u = \\cfrac{\\vv{\\text{v}}}{\\lvert \\vv{\\text{v}} \\rvert} = \\frac{(1,-1)}{\\sqrt{2}}= \\bm{\\left(\\frac{1}{\\sqrt{2}},-\\frac{1}{\\sqrt{2}} \\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"267\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-modulos-de-vectores\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78feb0de1149c92d8000673c3bd9c750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(6,8)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2223831dac0e96dc39b2c1f575a96656_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert\\vv{a} \\rvert= \\sqrt{6^2+8^2} =\\sqrt{36+64} = \\sqrt{100} = \\bm{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u0423\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043e\u0442 \u0441\u0430\u043c\u043e\u0433\u043e \u043a\u043e\u0440\u043e\u0442\u043a\u043e\u0433\u043e \u043a \u0441\u0430\u043c\u043e\u043c\u0443 \u0434\u043b\u0438\u043d\u043d\u043e\u043c\u0443. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd5b4cce27e3e747335f1b83a27ea14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9528dc0e7c4fdec1f5ea0897cb5f1080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{b}=(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3d0c1b4ab12a00987c3821811108881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{c}=(5,12)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9611ddc072acda8752bf9cf38687c790_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{d}=(-6,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0414\u043b\u0438\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043d\u0430\u043c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u0438 \u0432\u0441\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f774b05c948e7cc2648508e840bec8d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\vv{a}\\right|= \\sqrt{4^2+(-2)^2} =\\sqrt{16+4} = \\sqrt{20}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"284\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26f7996534e539a7c403a494276e9b43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{b}|= \\sqrt{3^2+1^2} =\\sqrt{9+1} = \\sqrt{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"243\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41d80256e32169ae228c30631ed6a7c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix}\\vv{c}\\end{vmatrix}= \\sqrt{5^2+12^2} =\\sqrt{25+144} = \\sqrt{169} = 13\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"331\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8d50ea2580fbf8d44a19147ea34b730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{d}| = \\sqrt{(-6)^2+(-3)^2} =\\sqrt{36+9} = \\sqrt{45}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0435\u043d\u043d\u044b\u0435 \u043e\u0442 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0435\u0439 \u0434\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0435\u0439 \u0434\u043b\u0438\u043d\u044b (\u0438\u043b\u0438 \u043c\u043e\u0434\u0443\u043b\u044f): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e3ca300d8666eb94fd4ddd22088e00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{b}|< \\begin{vmatrix}\\vv{a}\\end{vmatrix} < |\\vv{d}| < \\begin{vmatrix}\\vv{c}\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"144\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043d\u0430\u0447\u0430\u043b\u043e\u043c \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fa493d9071a18cc176e19c8aeda71e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0444\u0438\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0443\u043d\u043a\u0442\u0430 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7da7d69ba3de7c0a400c5739021b3ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(7,-4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0442\u0430\u0435\u043c \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u043c\u0438\u043d\u0443\u0441 \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-237f500f255108fb2f6673bdf1ac0c88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A=(7,-4)-(-3,2)=(10,-6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"337\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0437\u043d\u0430\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440, \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043c\u043e\u0434\u0443\u043b\u044f: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c92f7a1361051e25fa90e0ed878a676_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\vv{AB} \\end{vmatrix} =\\sqrt{10^2+(-6)^2} = \\sqrt{100+36}=\\bm{\\sqrt{136}}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"340\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u0420\u0430\u0437\u043b\u043e\u0436\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0438 \u043d\u0430\u0439\u0434\u0435\u043c \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-992e1cdc6a75b8bdfe860c97dc9911e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =8 \\qquad \\alpha = 45\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u043c\u043e\u0434\u0443\u043b\u044e, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0443\u0433\u043b\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33aa199d1341f57e7a85abaa3c261a91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_x= \\lvert \\vv{a}\\rvert \\cdot \\text{cos}(45\u00ba)= 8 \\cdot 0,71 = 5,66\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u0430 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u043c\u043e\u0434\u0443\u043b\u044f \u043d\u0430 \u0441\u0438\u043d\u0443\u0441 \u0443\u0433\u043b\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-269cf4eed12832856838538f0a314aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_y= \\lvert \\vv{a}\\rvert \\cdot \\text{sen}(45\u00ba)= 8 \\cdot 0,71 = 5,66\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9a4b542b5e7893c3da383ffa65a133b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{ = (5,66 \\ ,\\ 5,66)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0434\u0432\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0435 \u0438\u0434\u0435\u043d\u0442\u0438\u0447\u043d\u044b, \u0442\u043e \u0435\u0441\u0442\u044c \u0443\u0433\u043e\u043b \u043d\u0430\u043a\u043b\u043e\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 45\u00b0.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 5<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440 \u0441 \u0442\u0435\u043c \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c, \u0447\u0442\u043e \u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u043d\u043e \u0441 \u043c\u043e\u0434\u0443\u043b\u0435\u043c 1. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-764894932cc153ee326360c077c75ec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a} = (-4,3)\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412\u0435\u043a\u0442\u043e\u0440 \u0442\u043e\u0433\u043e \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u0442\u043e\u0433\u043e \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u043d\u043e \u0441 \u043c\u043e\u0434\u0443\u043b\u0435\u043c 1, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c. \u0427\u0442\u043e\u0431\u044b \u0435\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d067857f68bb43d3ee3693466272cc36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert=\\sqrt{(-4)^2+3^2} = \\sqrt{16+9} = \\sqrt{25} = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"315\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ff7322f3b35f78c5e151f4e7dc59eb98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{a}_u = \\cfrac{\\vv{a}}{\\lvert \\vv{a} \\rvert} = \\frac{(-4,3)}{5}= \\bm{\\left(-\\frac{4}{5},\\frac{3}{5} \\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"238\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 6<\/h3>\n<p> \u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e \u0440\u0430\u0437\u043b\u043e\u0436\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0435\u0433\u043e \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-305f67adc42d0194ae1c8bbca09484a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =6 \\qquad \\alpha = 20\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" 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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0430\u0437\u043b\u043e\u0436\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \u0438 \u043d\u0430\u0439\u0434\u0435\u043c \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-425294f0e8b14e63cf0d59c6fa95f367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_x= \\lvert \\vv{a}\\rvert \\cdot \\text{cos}(20\u00ba)= 6 \\cdot 0,94 = 5,64\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a795bfcb22419526d23f6d0ff419fdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_y= \\lvert \\vv{a}\\rvert \\cdot \\text{sen}(20\u00ba)= 6 \\cdot 0,34 = 2,05\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"266\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abc6fa01a5b562627b05dc37ad7f59d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}= (5,64 \\ ,\\ 2,05)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-287411b8f47ca842a6db2cbe1c9a6ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{a}_u = \\cfrac{\\vv{a}}{\\lvert \\vv{a} \\rvert} = \\frac{(5,64 \\ ,\\ 2,05)}{6}= \\bm{(0,94 \\ , \\ 0,34) }\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"318\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0440\u0430\u0432\u043d\u044b \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0443 \u0438 \u0441\u0438\u043d\u0443\u0441\u0443 \u0443\u0433\u043b\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u043d \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0441 \u043e\u0441\u044c\u044e X.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0435\u0435 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043c\u043e\u0434\u0443\u043b\u044c \u043f\u043e \u0434\u0432\u0443\u043c \u0442\u043e\u0447\u043a\u0430\u043c: \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u043e \u0438 \u043a\u043e\u043d\u0435\u0446. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043e \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044e \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043c\u043e\u0434\u0443\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0412\u044b \u0434\u0430\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c\u0438 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bc%d0%be%d0%b4%d1%83%d0%bb%d1%8c-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b8-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d1%8b-%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%80%d0%b5%d1%88\/\"> <span class=\"screen-reader-text\">\u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 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