{"id":222,"date":"2023-07-11T05:03:07","date_gmt":"2023-07-11T05:03:07","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%be%d1%80%d1%82%d0%be%d0%b3%d0%be%d0%bd%d0%b0%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%b5%d1%80%d0%bf%d0%b5%d0%bd%d0%b4%d0%b8%d0%ba%d1%83%d0%bb%d1%8f%d1%80%d0%bd%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/"},"modified":"2023-07-11T05:03:07","modified_gmt":"2023-07-11T05:03:07","slug":"%d0%be%d1%80%d1%82%d0%be%d0%b3%d0%be%d0%bd%d0%b0%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%b5%d1%80%d0%bf%d0%b5%d0%bd%d0%b4%d0%b8%d0%ba%d1%83%d0%bb%d1%8f%d1%80%d0%bd%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%be%d1%80%d1%82%d0%be%d0%b3%d0%be%d0%bd%d0%b0%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%b5%d1%80%d0%bf%d0%b5%d0%bd%d0%b4%d0%b8%d0%ba%d1%83%d0%bb%d1%8f%d1%80%d0%bd%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/","title":{"rendered":"\u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 (\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445) \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u0445: \u0447\u0442\u043e \u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0435, \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0434\u0440\u0443\u0433\u043e\u043c\u0443, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432&#8230; \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 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-vectores-perpendiculares-u-ortogonales\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\"> \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f <strong>\u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438<\/strong> (\u0438\u043b\u0438 <strong>\u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c\u0438<\/strong> ), \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0442 \u043f\u0440\u044f\u043c\u043e\u0439 \u0443\u0433\u043e\u043b (90\u00b0) \u0434\u0440\u0443\u0433 \u043a \u0434\u0440\u0443\u0433\u0443.<\/p>\n<p> \u041d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0434\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteurs-perpendiculaires-ou-orthogonaux.webp\" alt=\"\u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c\u0438 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438\" class=\"wp-image-1263\" width=\"195\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0441\u0442\u044c \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u0438\u0445 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u0430 \u043d\u0435 \u043e\u0442 \u0438\u0445 \u043c\u043e\u0434\u0443\u043b\u044f (\u0438\u043b\u0438 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b) \u0438\u043b\u0438, \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u043e\u0442 \u0438\u0445 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f. \u0422\u043e \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0431\u0443\u0434\u0443\u0442 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0443\u0433\u043e\u043b 90 \u0433\u0440\u0430\u0434\u0443\u0441\u043e\u0432, \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u0438\u043c\u0435\u044e\u0442 \u043b\u0438 \u043e\u043d\u0438 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0443\u044e \u0434\u043b\u0438\u043d\u0443. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-vectores-son-ortogonales-o-perpendiculares\"><\/span> \u041a\u0430\u043a \u0443\u0437\u043d\u0430\u0442\u044c, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u0438\u043b\u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u043c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0432\u0438\u0434\u0435\u043b\u0438, \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0447\u0435\u043d\u044c \u043b\u0435\u0433\u043a\u043e \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u043b\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u041e\u0434\u043d\u0430\u043a\u043e \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u043b\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043d\u0435 \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0430\u044f \u0438\u0445 \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435:<\/p>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\"> \u0427\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f <strong>\u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438<\/strong> \u0438\u043b\u0438 <strong>\u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c\u0438<\/strong> , \u0435\u0441\u043b\u0438 \u0438\u0445 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e (0).<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u043d\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0430\u044f \u0438\u0445 \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\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-54fd3ebc4e192bb4cbd2fbd0bcc42fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(3,2) \\qquad\\vv{\\text{v}}=(-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 (\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435) \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u043c  \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\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-73197e497b384965865651ffea4caea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\vv{\\text{u}} \\cdot \\vv{\\text{v}}&amp;=(3,2)\\cdot (-2,3) \\\\[1.5ex]&amp;=3\\cdot (-2) + 2 \\cdot 3 \\\\[1.5ex] &amp; = -6+6 \\\\[1.5ex] &amp; =\\bm{0} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, <strong>\u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u0442\u043e \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 (\u0438\u043b\u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435)<\/strong> \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\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-bfceefe77fc6ae5d21d70abf882f1d1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\bm{\\perp} \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u044b \u043a\u0430\u043a \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\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-519f18355ad2b09638ea0d45fce173fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\perp}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e. \u041e\u0434\u043d\u0430\u043a\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0435\u0449\u0435 \u043e\u0434\u0438\u043d \u0442\u0438\u043f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432) \u0434\u0430\u0435\u0442 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0435: \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0434\u0432\u0443\u043c \u0434\u0440\u0443\u0433\u0438\u043c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0430\u0436\u043d\u043e \u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u0442\u044c \u0434\u0432\u0430 \u0442\u0438\u043f\u0430 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u0432  \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f  . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-un-vector-perpendicular-u-ortogonal-a-otro\"><\/span> \u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0434\u0440\u0443\u0433\u043e\u043c\u0443? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\"> \u0421\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0434\u0440\u0443\u0433\u043e\u043c\u0443 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 (\u0432 R2), \u2014 \u044d\u0442\u043e \u0447\u0435\u0440\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0434\u0432\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043c\u0435\u043d\u044f\u0442\u044c \u0437\u043d\u0430\u043a \u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0443.<\/p>\n<p> \u0410 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u0434\u0440\u0443\u0433\u043e\u043c\u0443 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3), \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043e\u043f\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0434\u0432\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c, \u0437\u0430\u0442\u0435\u043c \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c \u0437\u043d\u0430\u043a \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043d\u0438\u0445 \u0438, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043e\u0431\u043d\u0443\u043b\u0438\u0442\u044c \u043e\u0441\u0442\u0430\u0432\u0448\u0443\u044e\u0441\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443.<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u0432 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438 \u043e\u0434\u043d\u043e\u0433\u043e \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0442 \u0434\u0440\u0443\u0433\u043e\u0433\u043e \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u043e\u0433\u043e, \u0438\u043c\u0435\u044e\u0442 \u043b\u0438 \u043e\u043d\u0438 2 \u0438\u043b\u0438 3 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b, \u0440\u0435\u0448\u0438\u043c \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u0442\u0438\u043f\u043e\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-un-vector-perpendicular-u-ortogonal-en-el-plano-cartesiano\"><\/span> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443:<\/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-e7317f02a44a1fe5e88995c6ab294552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0441\u0435\u0433\u043e \u0441 \u0434\u0432\u0443\u043c\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438, \u0442\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0447\u0435\u0440\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u044c \u043e\u0434\u043d\u0443 \u0438\u0437 \u043d\u0438\u0445:<\/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-318270e0576ad0c15e675699c6d746c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{=(-1,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u044d\u0442\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\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-1c66983a99e25383a527d0cfd895580f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\cdot \\vv{\\text{u}}=(4,1)\\cdot (-1,4) =0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-7c19152b46f64fc00ffc1240af05ff4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-un-vector-perpendicular-u-ortogonal-en-el-espacio-cartesiano\"><\/span> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443:<\/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-afaddd121c95f2c502c2016e71a574eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(2,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0442\u0440\u0435\u0445\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u043c\u0435\u043d\u044f\u0442\u044c \u043c\u0435\u0441\u0442\u0430\u043c\u0438 \u0434\u0432\u0435 \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b, \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c \u0437\u043d\u0430\u043a \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043d\u0438\u0445 \u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u043e\u0441\u0442\u0430\u0432\u0448\u0443\u044e\u0441\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443 \u0432 \u043d\u043e\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-222eeaab5108a26f483c091087a2b725_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{=(3,-2,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\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-e76a1a210d6c5eae392104e71390efbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\cdot \\vv{\\text{u}}=(2,3,-1)\\cdot (3,-2,0) =0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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-7c19152b46f64fc00ffc1240af05ff4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-vectores-perpendiculares-y-ortogonales\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438\u043c\u0435\u044e\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> <strong>\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0435 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f<\/strong> : \u0435\u0441\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0434\u0440\u0443\u0433\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443, \u0442\u043e \u044d\u0442\u043e\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u0442\u0430\u043a\u0436\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u043f\u0435\u0440\u0432\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443.<\/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-aa3a2053276b703b1f53c493b25311ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\bm{\\perp}  \\vv{\\text{v}} \\ \\longrightarrow \\ \\vv{\\text{v}} \\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"116\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0418\u0440\u0440\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u0432\u043d\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e<\/strong> : \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u043d\u0438 \u043e\u0434\u0438\u043d \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0441\u0430\u043c\u043e\u043c\u0443 \u0441\u0435\u0431\u0435.<\/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-153d5cde7f727d36c26bcca51f25980b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\ \\cancel{\\bm{\\perp}}} \\ \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0412 \u0435\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 (\u0432 R2) \u043b\u044e\u0431\u0430\u044f \u043f\u0430\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0442\u0440\u0435\u0442\u044c\u0435\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443, \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e\u0439. \u0422\u043e \u0435\u0441\u0442\u044c, \u0435\u0441\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0434\u0440\u0443\u0433\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0438 \u044d\u0442\u043e\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u0442\u0430\u043a\u0436\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0442\u0440\u0435\u0442\u044c\u0435\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443, \u043f\u0435\u0440\u0432\u044b\u0439 \u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b. \u042d\u0442\u043e \u0441\u0432\u044f\u0437\u0430\u043d\u043e \u0441  \u043f\u044f\u0442\u044b\u043c \u043f\u043e\u0441\u0442\u0443\u043b\u0430\u0442\u043e\u043c \u0415\u0432\u043a\u043b\u0438\u0434\u0430  .<\/li>\n<\/ul>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u0434\u043e\u043b\u0436\u043d\u044b \u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u0431\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u044d\u0442\u0438\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0448\u0442\u043e\u043f\u043e\u0440\u0430. \u042d\u0442\u043e\u0442 \u043c\u0435\u0442\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043b\u0435\u0433\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u0438\u043f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0431\u0435\u0437 \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0437\u0430\u043d\u044f\u043b\u043e \u0431\u044b \u043c\u043d\u043e\u0433\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438. \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0435, \u043c\u043e\u0436\u043d\u043e, \u043d\u0430\u0436\u0430\u0432 \u043d\u0430 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435  \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0448\u0442\u043e\u043f\u043e\u0440\u0430  . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"conceptos-relacionados-con-los-vectores-perpendiculares-u-ortogonales\"><\/span> \u041f\u043e\u043d\u044f\u0442\u0438\u044f, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0435 \u0441 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c\u0438 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u0432\u0430 \u0442\u0438\u043f\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u0438\u0445 \u043a \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c: \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u041e\u0440\u0442\u043e\u043c\u0430\u0440\u043b\u044f. \u0425\u043e\u0442\u044f \u0432\u0441\u0435 \u043e\u043d\u0438 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c, \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0443\u0442\u043e\u0447\u043d\u0438\u0442\u044c, \u0447\u0435\u043c \u043e\u043d\u0438 \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0439 \u043f\u0443\u0442\u0430\u043d\u0438\u0446\u044b.<\/p>\n<p> <strong>\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440<\/strong> \u2013 \u044d\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0433\u043e \u0442\u043e\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u043a\u043b\u044e\u0447\u0438\u0442\u044c \u0432 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043d\u043e \u0432 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043d \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0430 \u043d\u0435 \u0434\u0440\u0443\u0433\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0434\u0432\u0430 <strong>\u043e\u0440\u0442\u043e\u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> \u2014 \u044d\u0442\u043e \u0434\u0432\u0430 \u0432\u0437\u0430\u0438\u043c\u043d\u043e \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 (\u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b, \u0440\u0430\u0432\u043d\u043e\u0439 1).<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0442\u0430\u043a\u0436\u0435 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u043e\u0447\u0435\u043d\u044c \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f <strong>\u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0431\u0430\u0437\u0438\u0441\u044b<\/strong> (\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0435 \u0431\u0430\u0437\u0438\u0441\u044b, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0438\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0443) \u0438 \u0434\u0430\u0436\u0435 <strong>\u043e\u0440\u0442\u043e\u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0431\u0430\u0437\u0438\u0441\u044b<\/strong> . \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043e\u0442\u0441\u0447\u0435\u0442\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0440\u0442\u043e\u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u0431\u0430\u0437\u043e\u0439.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 (\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445) \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u0445: \u0447\u0442\u043e \u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0435, \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0439 \u0434\u0440\u0443\u0433\u043e\u043c\u0443, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432&#8230; \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 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430? \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438 (\u0438\u043b\u0438 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%be%d1%80%d1%82%d0%be%d0%b3%d0%be%d0%bd%d0%b0%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%b5%d1%80%d0%bf%d0%b5%d0%bd%d0%b4%d0%b8%d0%ba%d1%83%d0%bb%d1%8f%d1%80%d0%bd%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/\"> <span class=\"screen-reader-text\">\u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b<\/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":[22],"tags":[],"class_list":["post-222","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"<!-- This site is optimized 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content=\"\u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 (\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445) \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u0445: \u0447\u0442\u043e \u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0435, \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 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\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430? \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438 (\u0438\u043b\u0438 &hellip; \u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b 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