{"id":247,"date":"2023-07-10T14:01:40","date_gmt":"2023-07-10T14:01:40","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d1%8f%d0%b2%d0%bd%d0%be%d0%b5-%d0%be%d0%b1%d1%89%d0%b5%d0%b5-%d0%b8%d0%bb%d0%b8-%d0%b4%d0%b5%d0%ba%d0%b0%d1%80%d1%82%d0%be%d0%b2%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8\/"},"modified":"2023-07-10T14:01:40","modified_gmt":"2023-07-10T14:01:40","slug":"%d0%bd%d0%b5%d1%8f%d0%b2%d0%bd%d0%be%d0%b5-%d0%be%d0%b1%d1%89%d0%b5%d0%b5-%d0%b8%d0%bb%d0%b8-%d0%b4%d0%b5%d0%ba%d0%b0%d1%80%d1%82%d0%be%d0%b2%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d1%8f%d0%b2%d0%bd%d0%be%d0%b5-%d0%be%d0%b1%d1%89%d0%b5%d0%b5-%d0%b8%d0%bb%d0%b8-%d0%b4%d0%b5%d0%ba%d0%b0%d1%80%d1%82%d0%be%d0%b2%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8\/","title":{"rendered":"\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"},"content":{"rendered":"<p>\u041e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430), \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u043a\u0430\u043a \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. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0435\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u0438. \u0411\u043e\u043b\u0435\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 \u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-ecuacion-implicita-o-general-del-plano\"><\/span> \u041a\u0430\u043a\u043e\u0432\u043e \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\u043b\u0430\u043d\u0430? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\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>\u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/strong> , \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0435 <strong>\u043e\u0431\u0449\u0438\u043c<\/strong> \u0438\u043b\u0438 <strong>\u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b\u043c<\/strong> \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \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. \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \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\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u0430 \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<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-implicita-o-general-del-plano\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u0430\u043d\u0430 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> \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 style=\"text-align:left\"> \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 style=\"text-align:left;\"> \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-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<\/div>\n<p> \u0412\u0430\u0436\u043d\u043e, \u0447\u0442\u043e \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u043c\u0435\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f. \u0418 \u0447\u0442\u043e\u0431\u044b \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u043b\u043e\u0441\u044c, \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0435 \u0431\u044b\u043b\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b. <\/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=\"\u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \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 pan xy \u0432 r3\" class=\"wp-image-2443\" width=\"393\" height=\"138\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0425\u043e\u0442\u044f \u043d\u0435\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0437\u043d\u0430\u0442\u044c \u043f\u0440\u0438\u0447\u0438\u043d\u0443 \u044d\u0442\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0435\u0435 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044e \u043d\u0438\u0436\u0435.<\/p>\n<p> \u041e\u0442\u0442\u0430\u043b\u043a\u0438\u0432\u0430\u044f\u0441\u044c \u043e\u0442 \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\u043b\u0430\u043d\u0430, \u043f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u043d\u0435\u044f\u0432\u043d\u043e\u043c\u0443 (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u043c\u0443) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u043f\u043b\u0430\u043d\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-46f87775f11f01a59c70aa3ee864aebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\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}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u044b \u043f\u0435\u0440\u0435\u0434\u0430\u0435\u043c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0439 \u0447\u043b\u0435\u043d \u0438\u0437 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \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 \u0432 \u0434\u0440\u0443\u0433\u0443\u044e \u0447\u0430\u0441\u0442\u044c \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-0c2f3831ca03939d7e23d24c7d435337_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\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}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/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-aca0b16ff9b92401181c2bdc5ba981bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases} \\lambda \\text{u}_x + \\mu \\text{v}_x =x-P_x\\\\[1.7ex]  \\lambda \\text{u}_y + \\mu \\text{v}_y=y-P_y \\\\[1.7ex]  \\lambda\\text{u}_z + \\mu \\text{v}_z =z-P_z\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0432\u044b\u0448\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u043b\u0430 \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u043c\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u0440\u0430\u043d\u0433 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u0435\u043d 2 (\u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0420\u0443\u0448\u0430-\u0424\u0440\u043e\u0431\u0435\u043d\u0438\u0443\u0441\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-6f802b760ba5ab681afd0f02c83eddb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{pmatrix}\\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{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"142\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0441\u043b\u0438 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u0435\u043d \u0434\u0432\u0443\u043c, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3&#215;3 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\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-917f1770ff2a17897e5df76998ec3519_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> \u0418 \u0440\u0435\u0448\u0438\u0432 \u044d\u0442\u043e\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043e\u0431\u0449\u0435\u0435, \u043d\u0435\u044f\u0432\u043d\u043e\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:<\/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> \u0418\u0442\u0430\u043a, \u043c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043e\u0434\u043d\u0430\u043a\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0435\u0449\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \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\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0424\u043e\u0440\u043c\u0443\u043b\u0443 \u0438 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0432\u0441\u0435\u0445  \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u0430\u043d\u0430  \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043f\u043e \u044d\u0442\u043e\u0439 \u0441\u0441\u044b\u043b\u043a\u0435. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-ecuacion-implicita-o-general-del-plano\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \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\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0435\u044f\u0432\u043d\u043e\u0435 (\u0438\u043b\u0438 \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 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n<ul>\n<li> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2118d788ea1b10a70b36f284857de70e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u044b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef85b7409667d52ad3c9f8981dad5f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(2,0,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/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-a50e73125c9dcf4a9c58d316fbf850ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(4,-1,2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0438 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \u0442\u043e\u0447\u043a\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-917f1770ff2a17897e5df76998ec3519_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> \u0418\u0442\u0430\u043a, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438 \u0442\u043e\u0447\u043a\u0443 \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-aa25223c3a00e31f89043a3500d32c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}2 &amp; 4 &amp; x-3 \\\\[1.1ex]0 &amp; -1 &amp; y-1 \\\\[1.1ex]3&amp; 2 &amp; z-(-1) \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"173\" 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-7886f1c2758c204802b96f44acc8a7cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}2 &amp; 4 &amp; x-3 \\\\[1.1ex]0 &amp; -1 &amp; y-1 \\\\[1.1ex]3&amp; 2 &amp; z+1 \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"147\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3-\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0443 \u0421\u0430\u0440\u0440\u0443\u0441\u0430 \u0438\u043b\u0438 \u043f\u043e \u043a\u043e\u0444\u0430\u043a\u0442\u043e\u0440\u0430\u043c (\u0438\u043b\u0438 \u0437\u0430\u043c\u0435\u0441\u0442\u0438\u0442\u0435\u043b\u044f\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-3d8c2ae50c69efa75c6f439ec502a6d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2(z+1)+12(y-1)+3(x-3)-4(y-1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043e\u043f\u0435\u0440\u0438\u0440\u0443\u0435\u043c \u0438 \u0433\u0440\u0443\u043f\u043f\u0438\u0440\u0443\u0435\u043c \u0442\u0435\u0440\u043c\u0438\u043d\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e9cfe2d167a92bc1e64737ce9e7a5ed2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3(x-3)+8(y-1) -2(z+1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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-3cf3da637bf3a8d04fb2b8d791d78a9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-9+8y-8 -2z-2 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"223\" 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-65167b5921553dd9e11f9ac9bb80864e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+8y-2z-19 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \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\u043b\u0430\u043d\u0430 \u0442\u0430\u043a\u043e\u0432\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-152a3c9fd09fb72b6269201f02fb8303_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{3x+8y-2z-19 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-ecuacion-implicita-o-general-de-un-plano-a-partir-de-su-vector-normal\"><\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \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\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u043d\u043e\u0440\u043c\u0430\u043b\u0438.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0447\u0435\u043d\u044c \u0442\u0438\u043f\u0438\u0447\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u2014 \u043d\u0430\u0439\u0442\u0438, \u043a\u0430\u043a \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u0442\u043e\u0447\u043a\u0438 \u0438 \u0435\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e (\u0438\u043b\u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0433\u043e) \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0418\u0442\u0430\u043a, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u044d\u0442\u043e \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442.<\/p>\n<p> \u041d\u043e \u043f\u0440\u0435\u0436\u0434\u0435 \u0432\u0441\u0435\u0433\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e <strong>\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b X, Y, Z \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 <strong>\u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e<\/strong><\/strong> <strong>\u0441 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430\u043c\u0438 A, B, C \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0433\u043e) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \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-27f3ee5d7e81864550f3b86fdd53e89d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\color{orange} \\boxed{ \\color{black} \\quad \\pi : \\ Ax+By+C+D = 0 \\quad \\iff \\quad \\vv{n} = (A,B,C) \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"540\" style=\"vertical-align: -17px;\"><\/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-10affe1faee06a5faa4ef6d9c0473b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0432\u0435\u043a\u0442\u043e\u0440, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \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 \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0437\u043d\u0430\u0435\u043c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0437\u0430\u0434\u0430\u0447 \u0441 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438:<\/p>\n<ul>\n<li> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6df0e548515bb2b24f352853a2614015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u0435\u0433\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0435\u0441\u0442\u044c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44298f830c420011a4326017f5fd7cfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(3,-1,2) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e, \u043e\u0431\u0449\u0435\u0433\u043e \u0438\u043b\u0438 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \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-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> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b A, B \u0438 C, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u044b \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c \u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\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-596b3fdc65160234c06b0d28aebea74f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(3,-1,2) \\ \\longrightarrow \\ 3x-1y+2z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"322\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u043a\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 D. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0435\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-6df0e548515bb2b24f352853a2614015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-09a0b099394ba4634fb6d7aad3a627e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot 1-0+2\\cdot (-2)+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" 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-b90d57a1708925626a300c7e5db673ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3-4+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" 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-d2dfb99a77bfcee1b72540db9cf579a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"91\" 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-16ace3f6683252e5630a1091bbc0404e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \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\u043b\u0430\u043d\u0430 \u0442\u0430\u043a\u043e\u0432\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cde6db2f935eb7d0ad39141f86aab013_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{3x-y+2z+1 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"153\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-implicita-o-general-del-plano\"><\/span> \u0420\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0433\u043e \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><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \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\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b61f338575699a918d594595ddc6fb02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u044b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5150cc543174c7c079a38b016685eb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(4,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/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-0664398c6f1938e4ec5efaae48ab1c70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(5,3,-1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u0442\u0440\u0435\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0438 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \u0442\u043e\u0447\u043a\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-917f1770ff2a17897e5df76998ec3519_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 class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438 \u0442\u043e\u0447\u043a\u0443 \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-02e103601cd9992a8a8c087d016a08c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}4 &amp; 5 &amp; x+2 \\\\[1.1ex]1 &amp; 3 &amp; y-1 \\\\[1.1ex]3&amp; 1 &amp; z+1 \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b 3\u00d73 \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u044b\u043c \u0432\u0430\u043c\u0438 \u043c\u0435\u0442\u043e\u0434\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-ec35e71b9cca25aa9907c97da2ea2e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12(z+1)+15(y-1)+1(x+2)-9(x+2)-4(y-1)-5(z+1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0438 \u0433\u0440\u0443\u043f\u043f\u0438\u0440\u0443\u0435\u043c \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0447\u043b\u0435\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-fea5513ce57c88cac89a695b47b7a0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8(x+2)+11(y-1)+7(z+1) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" 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-b965060b2baad7f1b7fa66e0555a23f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x-16+11y-11+7z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"262\" 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-52635b24c2d396ff9a47fbd210c56bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x+11y+7z-20= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \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\u043b\u0430\u043d\u0430 \u0442\u0430\u043a\u043e\u0432\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc97887dad7e25ff823eee155fb58358_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-8x+11y+7z-20 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0442\u043e\u0447\u043a\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10de27107c1cf63dc889433e271d4a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u043f\u043b\u0430\u043d\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54a545de55c14f27d77bfda0188789a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi : \\ 2x+y+6z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"184\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0442\u043e\u0447\u043a\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u043b\u0430\u0441\u044c \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\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-25ef56f6218537e6592c6ce17e0c3cb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+y+6z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"153\" 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-10de27107c1cf63dc889433e271d4a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-b30e787cb2dfac5e87b0758b866e10a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (-1)+5+6\\cdot (-3)-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" 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-66acebc4d56a2fb70fe23b2ead99dcc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2+5-18-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"155\" 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-64706704bc6f3ef930293722159a8861_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-20\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"63\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\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, <strong>\u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043d\u0430 \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0430\u0441\u0442\u044c\u044e \u044d\u0442\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 (\u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u0430\u043d\u0430, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0435\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0442\u0440\u0438 \u0442\u043e\u0447\u043a\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-c3003c4a812ae18bebda7f61c0bbe5f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,-1,-2) \\qquad B(2,1,3) \\qquad C(4,1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"322\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\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, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u0418 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f \u0442\u0440\u0435\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f96add9ffd85a60c66b7b40a65192537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,1,3) - (5,-1,-2) = (-3,2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" 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-09c96a38b66a9b0108da71a2c7ea0b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (4,1,-2) - (5,-1,-2) = (-1,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"392\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0434\u0432\u0443\u0445 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043d\u0435 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043d\u0438 \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430.<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c \u0434\u0432\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0438 \u043e\u0434\u043d\u0443 \u0442\u043e\u0447\u043a\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0443\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043e\u0431\u0449\u0435\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-917f1770ff2a17897e5df76998ec3519_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 class=\"has-text-align-left\"> \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438 \u043e\u0434\u043d\u0443 \u0438\u0437 \u0442\u0440\u0451\u0445 \u0442\u043e\u0447\u0435\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-383093e607bc8ecc5f99e1815242b22a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix}-3 &amp; -1 &amp; x-5 \\\\[1.1ex]2 &amp; 2 &amp; y+1 \\\\[1.1ex]5&amp; 0 &amp; z+2 \\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"161\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\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-a3d7401055c280280af3a3d0486cdb86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6(z+2)-5(y+1)-10(x-5)+2(z+2)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" 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-4e355f06e9bd200804e0a37e059a389c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-10(x-5)-5(y+1)-4(z+2)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" 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-0f005d4a2fdd910e746e7231a1c83f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-10x+50-5y-5-4z-8=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"253\" 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-7653b13f379b9d38230f457c59d1a568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-10x-5y-4z+37=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u043d\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 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c\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-ac148d30ada4a3e256874712b4b196db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-10x-5y-4z+37=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<div class=\"wp-block-group\">\n<div class=\"wp-block-group__inner-container is-layout-flow\">\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \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\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e42bc8fa114f50a19858a526eabb6e30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u0435\u0433\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0435\u0441\u0442\u044c <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b007924d3ec5c7cd5de5d1d46cc86711_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(5,-2,-3) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e, \u043e\u0431\u0449\u0435\u0433\u043e \u0438\u043b\u0438 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u0430 \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-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 class=\"has-text-align-left\"> \u041d\u0443 \u0430 \u0438\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b A, B \u0438 C, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d\u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0440\u0430\u0432\u043d\u044b \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\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-8f4b71cc8d8c1610a5d5706ac44d1ad3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(5,-2,-3) \\ \\longrightarrow \\ 5x-2y-3z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0417\u043d\u0430\u0447\u0438\u0442 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 D. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0435\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-e42bc8fa114f50a19858a526eabb6e30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-720c689bc073e6c0f865bf406d92cbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5\\cdot 3-2\\cdot 4-3\\cdot (-3)+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" 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-3edf41b26a3b9c8bdead74d05767ec60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15-8+9+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"147\" 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-0db457697a3637eb92bff90460d8e98f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"16+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" 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-a2efb3d90e15e4474268d6de0570da4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=-16\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435, \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0438\u043b\u0438 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u0430\u043d\u0430 \u0442\u0430\u043a\u043e\u0432\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee0c114a24764dd24df9d58aab7155ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{5x-2y-3z-16 = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430), \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u043a\u0430\u043a \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. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0435\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u0438. \u0411\u043e\u043b\u0435\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 \u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u041a\u0430\u043a\u043e\u0432\u043e \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\u043b\u0430\u043d\u0430? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u043d\u0435\u044f\u0432\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 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0435 \u043e\u0431\u0449\u0438\u043c \u0438\u043b\u0438 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d1%8f%d0%b2%d0%bd%d0%be%d0%b5-%d0%be%d0%b1%d1%89%d0%b5%d0%b5-%d0%b8%d0%bb%d0%b8-%d0%b4%d0%b5%d0%ba%d0%b0%d1%80%d1%82%d0%be%d0%b2%d0%be-%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8\/\"> <span class=\"screen-reader-text\">\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<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[15],"tags":[],"class_list":["post-247","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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\u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0435\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u0438. \u0411\u043e\u043b\u0435\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 \u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u041a\u0430\u043a\u043e\u0432\u043e \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\u043b\u0430\u043d\u0430? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u043d\u0435\u044f\u0432\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 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0435 \u043e\u0431\u0449\u0438\u043c \u0438\u043b\u0438 &hellip; \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 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" 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