{"id":275,"date":"2023-07-10T00:23:44","date_gmt":"2023-07-10T00:23:44","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d1%80%d0%b0%d1%81%d1%81%d1%82%d0%be%d1%8f%d0%bd%d0%b8%d1%8f-%d0%be%d1%82-%d0%bb%d0%b8%d0%bd%d0%b8%d0%b8-%d0%b4%d0%be-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be\/"},"modified":"2023-07-10T00:23:44","modified_gmt":"2023-07-10T00:23:44","slug":"%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d1%80%d0%b0%d1%81%d1%81%d1%82%d0%be%d1%8f%d0%bd%d0%b8%d1%8f-%d0%be%d1%82-%d0%bb%d0%b8%d0%bd%d0%b8%d0%b8-%d0%b4%d0%be-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d1%80%d0%b0%d1%81%d1%81%d1%82%d0%be%d1%8f%d0%bd%d0%b8%d1%8f-%d0%be%d1%82-%d0%bb%d0%b8%d0%bd%d0%b8%d0%b8-%d0%b4%d0%be-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be\/","title":{"rendered":"\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-distancia-de-una-recta-a-un-plano\"><\/span> \u041a\u0430\u043a\u043e\u0432\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e?<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 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \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> \u0415\u0441\u043b\u0438 <strong>\u043b\u0438\u043d\u0438\u044f \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u0430 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c<\/strong> \u0438\u043b\u0438 \u0435\u0441\u043b\u0438 <strong>\u043b\u0438\u043d\u0438\u044f \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b<\/strong> , \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435, \u0440\u0430\u0437\u0434\u0435\u043b\u044f\u044e\u0449\u0435\u0435 \u0438\u0445, \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e.<\/li>\n<li> \u0415\u0441\u043b\u0438 <strong>\u043b\u0438\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> , \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438, \u0432\u0437\u044f\u0432 \u043b\u044e\u0431\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u043b\u0438\u043d\u0438\u0438 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0432 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. <\/li>\n<\/ul>\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\/distance-entre-une-ligne-et-un-plan.webp\" alt=\"\u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\" class=\"wp-image-4062\" width=\"459\" height=\"252\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432\u0430\u0436\u043d\u043e \u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c  \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e  \u0438 \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c  \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e  . \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 \u0432\u0430\u043c \u043d\u0435 \u0441\u043e\u0432\u0441\u0435\u043c \u043f\u043e\u043d\u044f\u0442\u043d\u043e \u0438\u043b\u0438 \u0432\u044b \u043d\u0435 \u0437\u043d\u0430\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0435\u043c \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0435 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b, \u0433\u0434\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u043f\u043e\u044f\u0441\u043d\u0435\u043d\u0438\u044f, \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-entre-una-recta-y-un-plano\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3), \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0440\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u0447\u0443:<\/p>\n<ul>\n<li> \u041a\u0430\u043a \u0434\u0430\u043b\u0435\u043a\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043b\u0438\u043d\u0438\u044f\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> \u043d\u0430 \u0441\u0430\u043c\u043e\u043b\u0435\u0442\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> ?<\/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-4785f2386b4ff9387b56cf8c5645c62d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}x=-2+t \\\\[1.7ex] y=1-3t \\\\[1.7ex] z=-1+2t\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d8872d79c59216f4a8489f75a751cdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi : \\ 4x+2y+z-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"184\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u0432\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0437\u043d\u0430\u0442\u044c \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438.<\/p>\n<p> \u0421 \u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043b\u0438\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0435\u0442\u0441\u044f \u0432 \u0432\u0438\u0434\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u0442\u043e\u0447\u043a\u0430, \u0447\u0435\u0440\u0435\u0437 \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043e\u043d\u0430 \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442, \u0440\u0430\u0432\u043d\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0765b71f9eead3b644fd5de150cdf321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{v}}_r =(1,-3,2) \\\\[2ex] P(-2,1,-1) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"154\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \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-f4fe9c16b8d08778c89ab62afcd8e34e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} =(4,2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u0437\u0430\u0438\u043c\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043b\u0438\u043d\u0438\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438 \u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \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-39d2d450c32a6fdf3182a3d16cc18116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{v}}_r \\cdot \\vv{n} &amp; = (1,-3,2) \\cdot (4,2,1) \\\\[2ex] &amp; = 1 \\cdot 4-3 \\cdot 2 +2\\cdot 1 \\\\[2ex] &amp;= 4 -6 +2 \\\\[2ex] &amp; = 0\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"202\" 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 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043b\u0438\u043d\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438\u043b\u0438 \u0431\u044b\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e\u0439 \u0435\u0439. \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u044f\u0441\u043d\u0438\u0442\u044c, \u043a\u0430\u043a\u043e\u0439 \u044d\u0442\u043e \u0441\u043b\u0443\u0447\u0430\u0439, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \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-e4916138781ab0b14c0b827b212fdd98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x+2y+z-6=0 \\ \\xrightarrow{P(-2,1,-1)} \\ 4\\cdot (-2) +2\\cdot 1 -1-6= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"460\" 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-15f3d9b73d0b2646f6d0173989e7b20a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8+2-1-6 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"146\" style=\"vertical-align: -2px;\"><\/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-d93d0450119c6530b10ed45266e017e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-13 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"63\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044f \u0442\u043e\u0447\u043a\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u043e\u0447\u043a\u0430 \u043d\u0435 \u043f\u043e\u0434\u0447\u0438\u043d\u044f\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u044f\u043c\u0430\u044f \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b.<\/p>\n<p> \u0417\u043d\u0430\u044f, \u0447\u0442\u043e \u043b\u0438\u043d\u0438\u044f \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \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-4413892ee4946e8c956d69a16a8d43ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,1,-1) \\qquad \\qquad \\pi: \\ 4x+2y+z-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"353\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \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-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0433\u043e \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-beb8f4629b0195d8ea0870d678585895_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 4\\cdot (-2)+2\\cdot 1+1\\cdot (-1)-6\\rvert}{\\sqrt{4^2+2^2+1^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"310\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-570743258f771c18a79b360b80b6a462_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -8+2-1-6\\rvert}{\\sqrt{16+4+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"204\" style=\"vertical-align: -16px;\"><\/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-3ea97bcf06817734423f2e6e662a1658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -13\\rvert}{\\sqrt{21}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"121\" style=\"vertical-align: -16px;\"><\/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-0a19bec182b20b9b1a5a08b41cd817c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{13}{\\sqrt{21}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"112\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0431\u044b\u043b\u043e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u043e\u043c\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82d2055df31134bca62040c367778b50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(r,\\pi)=d(P,\\pi) = }\\cfrac{\\bm{13}}{\\bm{\\sqrt{21}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"180\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0434\u043e\u043b\u0436\u043d\u043e \u0434\u0430\u0432\u0430\u0442\u044c \u043d\u0430\u043c \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u0432\u0441\u0435\u0433\u0434\u0430 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b. \u0415\u0441\u043b\u0438 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u0437\u043d\u0430\u0447\u0438\u0442, \u043c\u044b \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u043b\u0438 \u043e\u0448\u0438\u0431\u043a\u0443 \u043f\u0440\u0438 \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u0448\u0430\u0433\u0430.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u0438\u043d\u0438\u0438 \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f. \u041a\u0430\u043a\u043e\u0432\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u043d\u0438\u0435\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 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