{"id":253,"date":"2023-07-10T11:04:37","date_gmt":"2023-07-10T11:04:37","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d0%b0%d1%80%d0%b0%d0%bb%d0%bb%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be%d1%81%d1%82%d0%b8\/"},"modified":"2023-07-10T11:04:37","modified_gmt":"2023-07-10T11:04:37","slug":"%d0%bf%d0%b0%d1%80%d0%b0%d0%bb%d0%bb%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be%d1%81%d1%82%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d0%b0%d1%80%d0%b0%d0%bb%d0%bb%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be%d1%81%d1%82%d0%b8\/","title":{"rendered":"\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u0445: \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430,\u2026 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-planos-paralelos\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043d\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0438 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0438 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u043d\u0438\u0447\u0435\u0433\u043e \u043e\u0431\u0449\u0435\u0433\u043e.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-paralleles-1.webp\" alt=\"\u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439\" class=\"wp-image-2815\" width=\"332\" height=\"208\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0414\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e, \u043d\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u043c \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u043c\u0435\u0436\u0434\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3) \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0433\u0443\u0442 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0442\u044c\u0441\u044f \u0438\u043b\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0442\u044c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-planos-son-paralelos\"><\/span> \u041a\u0430\u043a \u0443\u0437\u043d\u0430\u0442\u044c, \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b \u043b\u0438 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0432\u0438\u0434\u0435\u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b \u043b\u0438 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438\u043b\u0438 \u043d\u0435\u0442.<\/p>\n<p> \u041d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u043e\u0431\u0449\u0435\u0433\u043e (\u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u043f\u043b\u0430\u043d\u043e\u0432:<\/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-679de3a47957678b36c7ce59c2ac3415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ A_1x+B_1y+C_1z+D_1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2685d26d2a3ccd531ef0fb45769d013a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A_2x+B_2y+C_2z+D_2 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0414\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0431\u0443\u0434\u0443\u0442 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0435\u0441\u043b\u0438 \u0438\u0445 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b A, B \u0438 C \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0443, \u0430 \u043d\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0443 D. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442, \u043a\u043e\u0433\u0434\u0430 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \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-10e8a78403a97a98ff8efc375d963d0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white ]}]{equation*}      \\cfrac{A_1}{A_2}=\\cfrac{B_1}{B_2} = \\cfrac{C_1}{C_2}\\neq \\cfrac{D_1}{D_2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-dos-planos-paralelos\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\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-83a8236303807a26eff03df9b5aae7ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x+2y-4z+1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" 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-99a5206f765bfb3f6441f5c41bba99dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+y-2z+5 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u041f\u043b\u0430\u043d\u044b \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u0440\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 X, Y, Z \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0443, \u0430 \u043d\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c \u0447\u043b\u0435\u043d\u0430\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-0dabd414a6a2dc053e2b91f27d89ab8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{3} =\\cfrac{2}{1} =\\cfrac{-4}{-2} \\neq \\cfrac{1}{5} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"261\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-distancia-entre-dos-planos-paralelos\"><\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0414\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043d\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u0437\u044f\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0434\u0432\u0443\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/strong> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \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 2 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0437\u043d\u0430\u0442\u044c  \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \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<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-deux-plans-paralleles.webp\" alt=\"\u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438\" class=\"wp-image-2647\" width=\"401\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u042d\u0442\u043e \u043c\u0435\u0442\u043e\u0434 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438. \u041e\u0434\u043d\u0430\u043a\u043e \u0435\u0441\u0442\u044c \u0435\u0449\u0435 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u044d\u0442\u043e, \u043a\u043e\u0433\u0434\u0430 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0410, \u0412 \u0438 \u0421 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0434\u0432\u0443\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442:<\/p>\n<p> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043e\u0431\u0449\u0438\u0435 (\u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u044b\u0435) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439:<\/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-a277aae741d0cfe8200b7c338f57343f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D_1=0 \\qquad \\qquad  \\pi_2 : \\ Ax+By+Cz+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"528\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> <strong>\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438<\/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-fba7a69f403ec1b933994e987e1ff71b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}} \\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"343\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a \u0447\u0442\u043e, \u043a\u043e\u043d\u0435\u0447\u043d\u043e, \u043b\u0435\u0433\u0447\u0435 \u043d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0432\u0441\u0435\u0433\u043e \u043b\u0438\u0448\u044c \u0432\u043e\u043f\u0440\u043e\u0441 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0438 \u0432\u0441\u0435, \u043d\u043e \u044d\u0442\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u0441\u0447\u0438\u0442\u0430\u0435\u043c, \u0447\u0442\u043e \u043b\u0443\u0447\u0448\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u043e\u0431\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u0442\u043e\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0432\u0430\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0440\u0430\u0432\u0438\u0442\u0441\u044f.<\/p>\n<h3 class=\"wp-block-heading\"> \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 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438<\/h3>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043c\u044b \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\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-a9cd1abd1a84a5a230fb855c75c59e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 4x-2y-4z+7=0 \\qquad \\qquad  \\pi_2 : \\ 8x-4y-8z+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"471\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0434\u0435\u043b\u043e \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u0441\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u0437\u0430 \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435\u043c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u043d\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\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-e13f3d3e18910312a6604d299010da6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{8}=\\cfrac{-2}{-4}=\\cfrac{-4}{-8}\\neq \\cfrac{7}{2} \\quad \\longrightarrow \\quad \\pi_1 \\parallel \\pi_2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0447\u043b\u0435\u043d\u044b \u0410, \u0412 \u0438 \u0421 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0434\u0432\u0443\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442, \u043d\u043e \u0434\u043e\u0431\u0438\u0442\u044c\u0441\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u043e\u0436\u043d\u043e, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u0432\u0441\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0442\u043e\u0440\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043d\u0430 \u0434\u0432\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-d159a803fe606b074b2fbafbf792829d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ \\cfrac{8x-4y-8z+2}{2}=\\cfrac{0}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"204\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0098cb52d72e1305e5cc6daee535dee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 4x-2y-4z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439 \u0442\u0435\u043f\u0435\u0440\u044c \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b A, B \u0438 C. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043b\u0435\u0433\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u043c\u0438:<\/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-3f78d3a0f1fd3a6c00acfd51c160dc8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert D_2-D_1\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"202\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0430\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-ebaa9342424e4e1c6df12cac1f2658fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 1-7\\rvert}{\\sqrt{4^2+(-2)^2+(-4)^2}}= \\cfrac{\\lvert -6\\rvert}{\\sqrt{36}} = \\cfrac{6}{6} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"369\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043e\u0434\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0438 \u0434\u0440\u0443\u0433\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0440\u0430\u0432\u043d\u043e \u0435\u0434\u0438\u043d\u0438\u0446\u0435. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-planos-paralelos\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435:<\/p>\n<ul>\n<li> <strong>\u0420\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u0432\u043d\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e<\/strong> : \u043a\u0430\u0436\u0434\u0430\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0441\u0430\u043c\u0430 \u0441\u0435\u0431\u0435.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0c49b095c95d593d607cda423172a99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\parallel \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438<\/strong> : \u0435\u0441\u043b\u0438 \u043e\u0434\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0434\u0440\u0443\u0433\u043e\u0439, \u0442\u043e \u0438 \u044d\u0442\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u043f\u0435\u0440\u0432\u043e\u0439. \u042d\u0442\u0438\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/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-6744d81df1ba01b40bf2dd2c429ead6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\parallel \\pi_2 \\ \\longrightarrow \\ \\pi_2 \\parallel \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0422\u0440\u0430\u043d\u0437\u0438\u0442\u0438\u0432\u043d\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e<\/strong> : \u0435\u0441\u043b\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0434\u0440\u0443\u0433\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0430 \u044d\u0442\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0442\u0440\u0435\u0442\u044c\u0435\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0442\u043e \u043f\u0435\u0440\u0432\u0430\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0442\u0430\u043a\u0436\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0442\u0440\u0435\u0442\u044c\u0435\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/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-cbdb26cf7c9104ca3111695826de0161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\pi_1 \\parallel \\pi_2\\\\[2ex] \\pi_2 \\parallel \\pi_3 \\end{array} \\right\\} \\longrightarrow \\ \\pi_1 \\parallel \\pi_3\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"176\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u0445: \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430,\u2026 \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043d\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0438 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0438 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u043d\u0438\u0447\u0435\u0433\u043e \u043e\u0431\u0449\u0435\u0433\u043e. \u0414\u0432\u0435 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d0%b0%d1%80%d0%b0%d0%bb%d0%bb%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d0%b5-%d0%bf%d0%bb%d0%be%d1%81%d0%ba%d0%be%d1%81%d1%82%d0%b8\/\"> <span class=\"screen-reader-text\">\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\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-253","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u2014 \u041c\u0430\u0442\u043e\u0440\u0438\u0442\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435-\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u2014 \u041c\u0430\u0442\u043e\u0440\u0438\u0442\u0438\" \/>\n<meta property=\"og:description\" content=\"\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044f\u0445: \u043a\u043e\u0433\u0434\u0430 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0435\u0439, \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430,\u2026 \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438? \u0412 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0432\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043d\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0438 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u0432\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f \u0438 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u043d\u0438\u0447\u0435\u0433\u043e \u043e\u0431\u0449\u0435\u0433\u043e. \u0414\u0432\u0435 &hellip; \u041f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\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\" content=\"https:\/\/mathority.org\/ru\/\u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0435-\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T11:04:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-paralleles-1.webp\" \/>\n<meta name=\"author\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" 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