{"id":223,"date":"2023-07-11T03:30:24","date_gmt":"2023-07-11T03:30:24","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b3%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d1%8f-%d0%bf%d1%80%d1%8f%d0%bc%d0%be%d0%b8\/"},"modified":"2023-07-11T03:30:24","modified_gmt":"2023-07-11T03:30:24","slug":"%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b3%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d1%8f-%d0%bf%d1%80%d1%8f%d0%bc%d0%be%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b3%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d1%8f-%d0%bf%d1%80%d1%8f%d0%bc%d0%be%d0%b8\/","title":{"rendered":"\u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445. \u0410 \u0435\u0449\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u044f\u043c\u043e\u0439 \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u0438\u0437 \u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. <\/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-la-ecuacion-vectorial-de-la-recta\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 \u2014 \u044d\u0442\u043e \u043d\u0430\u0431\u043e\u0440 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u0432 \u043e\u0434\u043d\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0431\u0435\u0437 \u043a\u0440\u0438\u0432\u044b\u0445 \u0438\u043b\u0438 \u0443\u0433\u043b\u043e\u0432. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> \u0418\u0442\u0430\u043a, <strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> \u2014 \u044d\u0442\u043e \u0441\u043f\u043e\u0441\u043e\u0431 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u043b\u0438\u043d\u0438\u044e. \u0418 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0442\u043e\u0447\u043a\u0438, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-la-ecuacion-vectorial-de-la-recta\"><\/span> \u041a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> \u0410\u0433\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-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> &#8212; \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438 \u0438<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u043e\u0447\u043a\u0430, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0430\u044f \u043f\u0440\u0430\u0432\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-798c10bf651dde568bef6722fc25cef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2) \\qquad P(P_1,P_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 <strong>\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438<\/strong> :<\/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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px;\"> \u0417\u043e\u043b\u043e\u0442\u043e:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u2014 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/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-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u2014 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0430\u0441\u0442\u044c\u044e \u043b\u0438\u043d\u0438\u0438.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/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-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u044f\u043c\u043e\u0439.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2014 \u0441\u043a\u0430\u043b\u044f\u0440 (\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e), \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u044f\u043c\u043e\u0439. <\/li>\n<\/ul>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\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\/equations-de-la-droite-1.webp\" alt=\"\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 4, \u043a\u043e\u0442\u043e\u0440\u043e\u0435\" class=\"wp-image-1304\" width=\"281\" height=\"268\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u042d\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u0438 \u0440\u0430\u0431\u043e\u0442\u0435 \u0441 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 2-\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 (\u0432 R2). \u041e\u0434\u043d\u0430\u043a\u043e \u0435\u0441\u043b\u0438 \u0431\u044b \u043c\u044b \u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043b\u0438 \u0440\u0430\u0441\u0447\u0435\u0442\u044b \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3), \u043d\u0430\u043c \u043f\u0440\u0438\u0448\u043b\u043e\u0441\u044c \u0431\u044b \u0434\u043e\u0431\u0430\u0432\u0438\u0442\u044c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0443\u044e:<\/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-3ef53596406b2fe36258a0421c91336b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_1,P_2,P_3)+t\\cdot (\\text{v}_1,\\text{v}_2,\\text{v}_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0438\u043c\u0435\u0439\u0442\u0435 \u0432 \u0432\u0438\u0434\u0443, \u0447\u0442\u043e \u043f\u043e\u043c\u0438\u043c\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438: \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043d\u0435\u044f\u0432\u043d\u043e\u0435 (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0447\u043a\u0438-\u043d\u0430\u043a\u043b\u043e\u043d\u0430 \u043b\u0438\u043d\u0438\u0438. . \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0432\u0441\u0435  \u0442\u0438\u043f\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0432 \u0441\u0442\u0440\u043e\u043a\u0435  \u043c\u043e\u0436\u043d\u043e \u043f\u043e \u044d\u0442\u043e\u0439 \u0441\u0441\u044b\u043b\u043a\u0435. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-ecuacion-vectorial-de-la-recta\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439 <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> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n<ul>\n<li> \u041d\u0430\u043f\u0438\u0448\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u0438\u043c\u0435\u0435\u0442<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043a\u0430\u043a \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440:<\/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-c4f245fcb7cc0cea584213b379d0cc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (1,2) \\qquad P(3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438, \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u0435 \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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-d4d382959b5006597c30376b200d167f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,0)+t\\cdot (1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"obtener-puntos-a-partir-de-la-ecuacion-vectorial-de-la-recta\"><\/span> \u041f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0435 \u0442\u043e\u0447\u0435\u043a \u0438\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e \u043a\u0430\u043a \u043c\u044b \u043d\u0430\u0448\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438, \u043e\u0447\u0435\u043d\u044c \u043b\u0435\u0433\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0438, \u0447\u0435\u0440\u0435\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u043b\u0438\u043d\u0438\u044f. \u0427\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u043b\u0438\u043d\u0438\u0438 <strong>, \u043f\u0440\u043e\u0441\u0442\u043e \u0437\u0430\u0434\u0430\u0439\u0442\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0443<\/strong><\/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-50d6971192a73f12b183dbddd7c75197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{t}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u044f\u043c\u043e\u0439.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0434\u0430\u043d\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438:<\/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-cd6dd1a3c3a001280f7fc7d94713c2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(1,-1)+t\\cdot (2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041e\u0447\u043a\u043e \u043d\u0430\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u0437\u0430 \u0437\u0430\u043c\u0435\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u043e \u043b\u044e\u0431\u043e\u043c\u0443 \u043d\u043e\u043c\u0435\u0440\u0443, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/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-81a04a05d8ea6730567685bff8148959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+1\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(2,3) \\\\[2ex] &amp; = (1+2 \\ , -1+3) \\\\[2ex] &amp; = \\bm{(3,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0435\u0449\u0435 \u043e\u0434\u043d\u0443 \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u043b\u0438\u043d\u0438\u0438, \u0434\u0430\u044e\u0449\u0443\u044e \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0434\u0440\u0443\u0433\u043e\u0439 \u043d\u043e\u043c\u0435\u0440, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/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-70cfec547c993eddfea11d50bef03bae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+2\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(4,6) \\\\[2ex] &amp; = (1+4 \\ , -1+6) \\\\[2ex] &amp; = \\bm{(5,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0442\u043e\u0447\u0435\u043a \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043c\u043e\u0436\u0435\u0442 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-vectorial-de-la-recta\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u044f\u043c\u043e\u0439<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> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\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-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u0447\u0435\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u0435\u043d <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80c361259467f8dee47e246c764ef897_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/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-b5adb01b1c1b8426314e6158a3ad6ff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,3) \\qquad \\vv{\\text{v}}=(4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"188\" 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 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438, \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u0435 \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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" 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> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0442\u0440\u0438 \u0442\u043e\u0447\u043a\u0438, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0438\u0435\u0441\u044f \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438\u0437 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0437\u0430\u0434\u0430\u0447\u0438. <\/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\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u0435\u043a \u0438\u0437 \u043b\u0438\u043d\u0438\u0438, \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u043c\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0437\u0430\u0434\u0430\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u043e\u0435 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0437\u0430\u0434\u0430\u0447\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-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0442\u043e\u0447\u043a\u0438 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u043e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/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-36452411cca47b72db95b2876b03f69d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+1\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (4,-2) \\\\[2ex] &amp; = (-1+4 \\ , 3-2) \\\\[2ex] &amp; = \\bm{(3,1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0432\u0442\u043e\u0440\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0434\u0430\u0434\u0438\u043c<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/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-5a5fe3c08ab62695f62cf76df97aac2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+2\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (8,-4) \\\\[2ex] &amp; = (-1+8 \\ , 3-4) \\\\[2ex] &amp; = \\bm{(7,-1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0442\u0440\u0435\u0442\u0438\u0439 \u043f\u0443\u043d\u043a\u0442, \u043f\u0440\u0438\u0441\u0432\u0430\u0438\u0432\u0430\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-063c366f7c1d1f7a8a92c459c8c495d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=3:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/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-9710aef8527fc6c53d21109ea01a1b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+3\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (12,-6) \\\\[2ex] &amp; = (-1+12 \\ , 3-6) \\\\[2ex] &amp; = \\bm{(11,-3)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0432\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0440\u0430\u0437\u043d\u044b\u0435 \u0431\u0430\u043b\u043b\u044b, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u044b \u0434\u0430\u0435\u0442\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u041d\u043e \u0435\u0441\u043b\u0438 \u0432\u044b \u043f\u0440\u043e\u0434\u0435\u043b\u0430\u043b\u0438 \u0442\u0443 \u0436\u0435 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0443, \u0432\u0441\u0435 \u0432 \u043f\u043e\u0440\u044f\u0434\u043a\u0435.<\/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> \u0418\u043b\u0438 \u0434\u0432\u0430 \u043f\u0443\u043d\u043a\u0442\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-39e1ccbebf7e7d41e0c9bc87567a83c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,1) \\qquad B(3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u044d\u0442\u0438 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438. <\/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 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0443 \u043d\u0430\u0441 \u043d\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440 \u0435\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u0430 \u0437\u0430\u0442\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c\u044b\u0439 \u0434\u0432\u0443\u043c\u044f \u0437\u0430\u0434\u0430\u043d\u043d\u044b\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438:<\/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-2ef2698c8dcca35e09a5fbbb3c07bdcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A= (3,-2)- (5,1) = (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043e \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0437\u0430\u0434\u0430\u043d\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a \u0438 \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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-68960ac44d082e7f07e54f954e16ac41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(5,1)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u0443\u0442\u0435\u043c \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u0440\u0443\u0433\u043e\u0439 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u0442\u0430\u043a\u0436\u0435 \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432\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-a3931a59d4987a867d7e380fe782df9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,-2)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"224\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445. \u0410 \u0435\u0449\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u044f\u043c\u043e\u0439 \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u0438\u0437 \u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439? \u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438 \u2014 \u044d\u0442\u043e \u043d\u0430\u0431\u043e\u0440 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u0432 \u043e\u0434\u043d\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0431\u0435\u0437 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b3%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d1%8f-%d0%bf%d1%80%d1%8f%d0%bc%d0%be%d0%b8\/\"> <span class=\"screen-reader-text\">\u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &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":[15],"tags":[],"class_list":["post-223","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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