{"id":268,"date":"2023-07-10T04:04:14","date_gmt":"2023-07-10T04:04:14","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%b0%d1%8f-%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f\/"},"modified":"2023-07-10T04:04:14","modified_gmt":"2023-07-10T04:04:14","slug":"%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%b0%d1%8f-%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%b0%d1%8f-%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f\/","title":{"rendered":"\u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c (\u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f)"},"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 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u043a\u0430\u043a \u043e\u043d\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438 \u0432\u0441\u0435 \u0435\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430. \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u043a\u0430\u043a\u043e\u0432\u044b \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0438, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043a\u0430\u043a \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-plano\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u043b\u0430\u043d?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<p> <strong>\u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u2013 \u044d\u0442\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043e\u0431\u044a\u0435\u043a\u0442, \u0438\u043c\u0435\u044e\u0449\u0438\u0439 \u0434\u0432\u0430 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f (\u0434\u043b\u0438\u043d\u0443 \u0438 \u0448\u0438\u0440\u0438\u043d\u0443).<\/strong> <\/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\/quel-est-l-avion.webp\" alt=\"\u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\" class=\"wp-image-3433\" width=\"417\" height=\"203\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043b\u0438\u043d\u0438\u0438 \u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438. \u0412 \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\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0440\u0430\u0437\u043d\u0438\u0446\u0443 \u043c\u0435\u0436\u0434\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u0442\u043e\u0447\u043a\u043e\u0439. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u0441\u0442\u0440\u043e\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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u043a\u043e\u043d\u0447\u0438\u043a<\/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> \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0442\u0441\u044f \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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\u043b\u0430\u043d\u0435, \u043f\u043b\u0430\u043d\u044b \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0431\u0443\u043a\u0432\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-fdef793ea5450647d6139c80d45be77a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi, \\alpha, \\beta,...\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"71\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u0438\u043c\u0435\u0440\u043e\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c. \u0414\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u2014 \u044d\u0442\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c\u0430\u044f \u043e\u0441\u044c\u044e \u0430\u0431\u0441\u0446\u0438\u0441\u0441 (\u043e\u0441\u044c X) \u0438 \u043e\u0441\u044c\u044e \u043e\u0440\u0434\u0438\u043d\u0430\u0442 (\u043e\u0441\u044c Y). \u041e\u0434\u043d\u043e \u0438\u0437 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0439 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0437\u0430\u043a\u043b\u044e\u0447\u0430\u0435\u0442\u0441\u044f \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u043e\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043e\u0431\u044a\u0435\u043a\u0442\u0430 \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u043e\u0442\u0441\u0447\u0435\u0442\u0430.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinacion-de-un-plano\"><\/span>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u043b\u0430\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u043f\u043e\u043d\u044f\u043b\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0432 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3).<\/p>\n<p> \u041f\u043b\u0430\u043d \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438:<\/p>\n<ul>\n<li> \u0422\u0440\u0438 \u0442\u043e\u0447\u043a\u0438 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442.<\/li>\n<li> \u041f\u0440\u044f\u043c\u0430\u044f \u043b\u0438\u043d\u0438\u044f \u0438 \u0442\u043e\u0447\u043a\u0430 \u0441\u043d\u0430\u0440\u0443\u0436\u0438.<\/li>\n<li> \u0414\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u044f\u043c\u044b\u0435 \u0438\u043b\u0438 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u043b\u0438\u043d\u0438\u0438.<\/li>\n<\/ul>\n<p> \u0427\u0442\u043e \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u043f\u0443\u043d\u043a\u0442\u0430, \u0432\u044b, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e, \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0434\u0432\u0435 \u043f\u0440\u044f\u043c\u044b\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b. \u041d\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0441\u0435\u043a\u0443\u0449\u0438\u0445 \u043b\u0438\u043d\u0438\u0439 \u043c\u0435\u043d\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u044b, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0437\u043d\u0430\u0442\u044c  , \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u0435\u043a\u0443\u0449\u0438\u0435 \u043b\u0438\u043d\u0438\u0438  .<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043a\u0430\u043a\u043e\u0435-\u043b\u0438\u0431\u043e \u0438\u0437 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0445 3-\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u0439, \u0437\u043d\u0430\u0447\u0438\u0442, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043f\u043b\u0430\u043d.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-plano\"><\/span> \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u043b\u0430\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u043b\u0430\u043d \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0430\u043c:<\/p>\n<ul>\n<li> \u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \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.<\/li>\n<li> \u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u0438\u043d\u0438\u0439.<\/li>\n<li> \u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0431\u0435\u0437\u0433\u0440\u0430\u043d\u0438\u0447\u043d\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u044d\u0442\u043e \u043f\u043e\u0432\u0435\u0440\u0445\u043d\u043e\u0441\u0442\u044c, \u043f\u0440\u043e\u0441\u0442\u0438\u0440\u0430\u044e\u0449\u0430\u044f\u0441\u044f \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0431\u0435\u0437 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439.<\/li>\n<li> \u0414\u0432\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442 \u043b\u0438\u043d\u0438\u044e.<\/li>\n<li> \u041b\u0438\u043d\u0438\u044f, \u0438\u043c\u0435\u044e\u0449\u0430\u044f \u0442\u043e\u0447\u043a\u0443 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442\u0441\u044f \u0442\u0430\u043c. \u0427\u0442\u043e\u0431\u044b \u043b\u0438\u043d\u0438\u044f \u0431\u044b\u043b\u0430 \u0447\u0430\u0441\u0442\u044c\u044e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043e\u043d\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0438\u043c\u0435\u0442\u044c \u0445\u043e\u0442\u044f \u0431\u044b \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/li>\n<li> \u0411\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442 \u043f\u0440\u044f\u043c\u0443\u044e.<\/li>\n<li> \u041f\u043e\u043b\u0443\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u2014 \u044d\u0442\u043e \u043a\u0430\u0436\u0434\u0430\u044f \u0438\u0437 \u0434\u0432\u0443\u0445 \u0447\u0430\u0441\u0442\u0435\u0439, \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0430\u0437\u0431\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0440\u0438 \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u043d\u0438\u0438 \u0435\u0435 \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0435\u0435 \u043f\u0440\u044f\u043c\u044b\u0445. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-del-plano\"><\/span> \u043f\u043b\u043e\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 <strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0435\u0435 \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 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c. \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0443\u0436\u043d\u0430 \u0432\u0441\u0435\u0433\u043e \u043b\u0438\u0448\u044c \u0442\u043e\u0447\u043a\u0430 \u0438 \u0434\u0432\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0445 \u044d\u0442\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. <\/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\/equations-planes.webp\" alt=\"\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 xy\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e, \u043a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432\u044b\u0448\u0435 \u043f\u0440\u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043f\u043b\u0430\u043d\u0430, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u043b\u0430\u043d\u0430. \u041d\u0443, \u0442\u043e\u0447\u043d\u043e \u0442\u0430\u043a \u0436\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0440\u0430\u0437\u043d\u044b\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 \u043f\u043b\u0430\u043d\u0430.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u0441\u0435\u043c\u0438 \u0442\u0438\u043f\u0430\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f: <strong>\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> , <strong>\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong> , <strong>\u043d\u0435\u044f\u0432\u043d\u043e\u0435 (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u0438 <strong>\u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 (\u0438\u043b\u0438 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u043d\u043e\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/p>\n<p> \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0443\u0432\u0438\u0434\u0438\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0432\u0441\u0435\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u0430\u043d\u0430. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-vectorial-del-plano\"><\/span> \u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u043e\u0447\u043a\u0443 \u0438 \u0434\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-d9227901692832cb0c176a896d35e896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      (x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418\u043b\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\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-78b41d21b63c22ec05d3f93576a897e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+\\lambda (\\text{u}_x,\\text{u}_y,\\text{u}_z) + \\mu (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"398\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> \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-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0434\u0432\u0430 \u0441\u043a\u0430\u043b\u044f\u0440\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-parametricas-del-plano\"><\/span> \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 <strong>\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-e1791802331aa9973126b3d7c7f1b716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \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-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0434\u0432\u0430 \u0441\u043a\u0430\u043b\u044f\u0440\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430.<\/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-0b77e9af6839a6bc60da39dd1798dd6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_x,\\text{u}_y,\\text{u}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u043b\u0430\u043d\u0430<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8a3eef2109d6a80a337c88337a1443e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -6px;\"><\/p>\n<\/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-f61b32275ccdbca7f8d5e0b3c750dd35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_x,\\text{v}_y,\\text{v}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u0434\u0440\u0443\u0433\u043e\u0433\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043b\u0430\u043d\u0430 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75c6a57a037206319f16dec389993ded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -6px;\"><\/p>\n<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-implicita-o-general-del-plano\"><\/span> \u041d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u043e\u0447\u043a\u0443 \u0438 \u0434\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041d\u0435\u044f\u0432\u043d\u043e\u0435, \u043e\u0431\u0449\u0435\u0435 \u0438\u043b\u0438 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043f\u0443\u0442\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044f \u0438 \u043f\u0440\u0438\u0441\u0432\u043e\u0435\u043d\u0438\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430, \u0440\u0430\u0432\u043d\u043e\u0433\u043e 0:<\/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-68d67612dfa54d76666aa37b702a472f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}\\text{u}_x &amp; \\text{v}_x &amp; x-P_x \\\\[1.1ex]\\text{u}_y &amp; \\text{v}_y &amp; y-P_y \\\\[1.1ex]\\text{u}_z &amp; \\text{v}_z &amp; z-P_z \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <strong>\u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u043b\u0430\u043d\u0430<\/strong> \u0431\u0443\u0434\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\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-7dcacf16123986ecd33dace4f4411914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle Ax+By+Cz+D=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e\u0442 \u0442\u0438\u043f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-o-segmentaria-del-plano\"><\/span> \u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438\u043b\u0438 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0438\u043b\u0438 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0438\u0434:<\/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-7c19853d465a703aa398bde04fa3222c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\cfrac{x}{a}+\\cfrac{y}{b} + \\cfrac{z}{c} = 1  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2014 \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043e\u0441\u0438 X.<\/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-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2014 \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043e\u0441\u0438 Y.<\/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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0417\u0434\u0435\u0441\u044c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u043e\u0441\u044c Z. <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435) \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0438\u0437 \u0435\u0435 \u043e\u0431\u0449\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\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-27e298e3103f917bd81b20315b6d9025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"183\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0435\u0448\u0430\u0435\u043c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 D \u0438\u0437 \u0443\u0440\u0430\u0432\u043d\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-7e6829185741f883a29bf004cbf570a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz=-D\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"166\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0417\u0430\u0442\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u0432\u0441\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u0430\u043d\u0430 \u043d\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 D, \u0438\u0437\u043c\u0435\u043d\u0438\u0432\u0448\u0435\u0433\u043e \u0437\u043d\u0430\u043a:<\/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-04843e22b4176c0ce921483f93dffeab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax+By+Cz}{-D}=\\cfrac{-D}{-D}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"176\" style=\"vertical-align: -12px;\"><\/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-278ce62f85ca44612254f48e96154726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax}{-D}+\\cfrac{By}{-D}+\\cfrac{Cz}{-D}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"166\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0418, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0434\u0440\u043e\u0431\u0435\u0439, \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u043c \u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\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-a58254e773c7c14b5b337a4330997125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{-\\frac{D}{A}}+\\cfrac{y}{-\\frac{D}{A}}+\\cfrac{z}{-\\frac{D}{A}}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"167\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u044b\u0432\u043e\u0434\u0438\u043c \u0438\u0437 \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0447\u043b\u0435\u043d\u044b \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0438\u043b\u0438 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-86975df14352b1b0c2ca05d2daaf40f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=-\\cfrac{D}{A} \\qquad b=-\\cfrac{D}{B} \\qquad c=-\\cfrac{D}{C}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"260\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u044d\u0442\u043e\u0442 \u0432\u0430\u0440\u0438\u0430\u043d\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u0430\u043d\u0430, \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0410, \u0412 \u0438 \u0421 \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043e\u0442\u043b\u0438\u0447\u043d\u044b \u043e\u0442 \u043d\u0443\u043b\u044f, \u0447\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u0434\u0440\u043e\u0431\u0435\u0439. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"posicion-relativa-de-dos-planos\"><\/span> \u0412\u0437\u0430\u0438\u043c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u0440\u0438 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438: \u0441\u0435\u043a\u0443\u0449\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0449\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/p>\n<ul>\n<li> <strong>\u041f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> : \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e \u043e\u0434\u043d\u043e\u0439 \u043b\u0438\u043d\u0438\u0438.<\/li>\n<li> <strong>\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> : \u0414\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u043d\u0438 \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/li>\n<li> <strong>\u0421\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0449\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> : \u0414\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442, \u0435\u0441\u043b\u0438 \u0432\u0441\u0435 \u043e\u043d\u0438 \u0438\u043c\u0435\u044e\u0442 \u043e\u0431\u0449\u0438\u0435 \u0442\u043e\u0447\u043a\u0438. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-30\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>\u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> <\/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\/plans-secants.webp\" alt=\"\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0445\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439\" class=\"wp-image-2814\" width=\"265\" height=\"258\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>\u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> <\/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\/plans-paralleles-1.webp\" alt=\"\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439\" class=\"wp-image-2815\" width=\"266\" height=\"166\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>\u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0449\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> <\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/deux-avions-coincidents.webp\" alt=\"\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0449\u0438\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439\" class=\"wp-image-2820\" width=\"294\" height=\"83\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0435\u0441\u043b\u0438 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u043f\u043e\u0434 \u0443\u0433\u043b\u043e\u043c 90\u00b0, \u044d\u0442\u043e \u0434\u0432\u0435 <strong>\u0432\u0437\u0430\u0438\u043c\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"angulo-entre-dos-planos\"><\/span> \u0423\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0440\u0430\u0432\u0435\u043d \u0443\u0433\u043b\u0443, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u0435\u0439 \u043a \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>\u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0443\u0433\u043b\u0430 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u0433\u043e\u043b, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u0435\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u044b.<\/strong><\/p>\n<p> \u0418\u0442\u0430\u043a, \u0440\u0430\u0437 \u0443\u0436 \u043c\u044b \u0442\u043e\u0447\u043d\u043e \u0437\u043d\u0430\u0435\u043c, \u0438\u0437 \u0447\u0435\u0433\u043e \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0443\u0433\u043b\u0430 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0438\u0437 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0443\u0433\u043b\u0430 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438:<\/p>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u0431\u0449\u0435\u0435 (\u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\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-dfa3d7e6f1ece8353327be7c9227d75b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ A_1x+B_1y+C_1z+D_1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/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-2c3966346685421fe3e535cf57a5491d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A_2x+B_2y+C_2z+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043a\u0430\u0436\u0434\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\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-eb0ca06882e0d61d6f8134368946ef29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1=(A_1,B_1,C_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" 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-22fba6a063a544bdf257e64d8d139238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2=(A_2,B_2,C_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0410 \u0443\u0433\u043e\u043b, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u044d\u0442\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0443\u0442\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0443\u0433\u043b\u0430, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u0435\u0439, \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \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-a0329572a30e8d75bd3795469fe65493_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0443\u0433\u043b\u0430, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u044c \u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0433\u043e \u0443\u0433\u043b\u0430.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u0438\u043b\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u043d\u0435\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e:<\/p>\n<ul>\n<li> \u0423\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0440\u0430\u0432\u0435\u043d 0\u00b0, \u0442\u0430\u043a \u043a\u0430\u043a \u0438\u0445 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435.<\/li>\n<li> \u0423\u0433\u043e\u043b \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 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0440\u0430\u0432\u0435\u043d 90\u00b0, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043d\u043e\u0440\u043c\u0430\u043b\u0435\u0439 \u0442\u0430\u043a\u0436\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b (\u0438\u043b\u0438 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b) \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0443 \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0442 \u043f\u0440\u044f\u043c\u043e\u0439 \u0443\u0433\u043e\u043b.<\/li>\n<\/ul>\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 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u043a\u0430\u043a \u043e\u043d\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438 \u0432\u0441\u0435 \u0435\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430. \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u043a\u0430\u043a\u043e\u0432\u044b \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0443\u0433\u043e\u043b \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0438, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043a\u0430\u043a \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u043b\u0430\u043d? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%b0%d1%8f-%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f\/\"> <span class=\"screen-reader-text\">\u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c (\u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 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