{"id":246,"date":"2023-07-10T13:20:19","date_gmt":"2023-07-10T13:20:19","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e7%82%b9%e5%88%b0%e5%b9%b3%e9%9d%a2%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e7%ad%94%e5%ae%9e%e4%be%8b%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T13:20:19","modified_gmt":"2023-07-10T13:20:19","slug":"%e7%a9%ba%e9%97%b4%e4%b8%ad%e7%82%b9%e5%88%b0%e5%b9%b3%e9%9d%a2%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e7%ad%94%e5%ae%9e%e4%be%8b%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e7%82%b9%e5%88%b0%e5%b9%b3%e9%9d%a2%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e7%ad%94%e5%ae%9e%e4%be%8b%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u7a7a\u95f4\u4e2d\u4e00\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u7a7a\u95f4\u4e2d\u7684\u70b9\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/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%bfcual-es-la-distancia-de-un-punto-a-un-plano\"><\/span>\u4e00\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u662f\u591a\u5c11\uff1f <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>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c<strong>\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u662f\u8be5\u70b9\u4e0e\u5e73\u9762\u4e0a\u4efb\u4f55\u5176\u4ed6\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8ddd\u79bb\u3002<\/strong>\u8be5\u8ddd\u79bb\u5bf9\u5e94\u4e8e\u4ece\u70b9\u5230\u5e73\u9762\u7684\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u7ebf\u6bb5\u7684\u957f\u5ea6\u3002 <\/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-dun-point-a-un-plan-de-formule.webp\" alt=\"\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u662f\u591a\u5c11\" class=\"wp-image-3471\" width=\"431\" height=\"227\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distancia-de-un-punto-a-un-plano\"><\/span>\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u516c\u5f0f<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<p>\u4e00\u65e6\u6211\u4eec\u51c6\u786e\u5730\u4e86\u89e3\u4e86\u70b9\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u6982\u5ff5\uff0c\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u8ba1\u7b97\u6240\u8ff0\u8ddd\u79bb\u7684\u516c\u5f0f\uff1a <\/p>\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\">\u7ed9\u5b9a\u4e00\u4e2a\u70b9\u548c\u5e73\u9762\u7684\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\uff1a<\/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-224b2b4bb57594d3fa92e148ada43cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x_0,y_0,z_0) \\qquad \\qquad \\pi: \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"><strong>\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u516c\u5f0f<\/strong>\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u70b9\u5230\u5e73\u9762\u8ddd\u79bb\u516c\u5f0f\u7684\u8bc1\u660e\u76f8\u5f53\u7e41\u7410\u4e14\u5197\u957f\uff0c\u56e0\u6b64\u6211\u4eec\u4e0d\u4f1a\u5728\u672c\u9875\u4e0a\u8fdb\u884c\u8bc1\u660e\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u5e94\u7528\u8be5\u516c\u5f0f\u65f6\u6211\u4eec\u5f97\u5230\u7684\u7ed3\u679c\u7b49\u4e8e\u96f6\uff0c\u8fd9\u663e\u7136\u610f\u5473\u7740\u8be5\u70b9\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a\u96f6\uff0c\u56e0\u6b64\u8be5\u70b9\u662f\u8be5\u5e73\u9762\u7684\u4e00\u90e8\u5206\u3002<\/p>\n<p>\u6700\u540e\uff0c\u8bf7\u6ce8\u610f\uff0c\u8981\u5e94\u7528\u8be5\u516c\u5f0f\uff0c\u5fc5\u987b\u5c06\u8ba1\u5212\u5b9a\u4e49\u4e3a\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u3002\u6240\u4ee5\u5982\u679c\u7528\u5176\u4ed6\u7c7b\u578b\u7684\u5e73\u9762\u65b9\u7a0b\u6765\u8868\u8fbe\uff0c\u6211\u4eec\u9996\u5148\u8981\u628a\u5b83\u8f6c\u5316\u4e3a\u4e00\u822c\u65b9\u7a0b\uff0c\u7136\u540e\u518d\u4f7f\u7528\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-de-un-punto-a-un-plano\"><\/span>\u8ba1\u7b97\u70b9\u5230\u5e73\u9762\u8ddd\u79bb\u7684\u793a\u4f8b<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>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u70b9\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u5982\u4f55\u7528\u6570\u503c\u786e\u5b9a\u7684\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u4e0b\u9762\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u70b9 P \u4e0e\u5e73\u9762 \u03c0 \u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u8bf4\u4e86\u8981\u70b9\u548c\u8ba1\u5212\uff1a<\/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-19db41565c49be8ca3580630de59813b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,3,-2) \\qquad \\qquad \\pi: \\ 2x+5y-4z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u627e\u5230\u4ece\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u53ea\u9700\u5e94\u7528\u4e0a\u4e00\u8282\u4e2d\u7684\u516c\u5f0f\u5373\u53ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u6bcf\u4e2a\u672a\u77e5\u6570\u7684\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-6c50799e6cbc0fb28d311858f4c94a82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2\\cdot 1+5\\cdot 3-4\\cdot (-2)+7\\rvert}{\\sqrt{2^2+5^2+(-4)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"282\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u8fdb\u884c\u64cd\u4f5c\uff1a<\/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-805821ed65a28cb8c08ee24473e8bd7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2+15+8+7\\rvert}{\\sqrt{4+25+16}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"199\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef28713d2c68c0bbb7a25bfd50466811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{32}}{\\bm{\\sqrt{45}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"107\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5206\u6570\u7684\u5206\u5b50\u6709\u7edd\u5bf9\u503c\uff0c\u5206\u6bcd\u6709\u5e73\u65b9\u6839\uff0c\u56e0\u6b64\u7ed3\u679c\u5fc5\u987b\u59cb\u7ec8\u4e3a\u6b63\u3002\u8fd9\u662f\u6709\u9053\u7406\u7684\uff0c\u56e0\u4e3a\u8ddd\u79bb\u4e0d\u80fd\u4e3a\u8d1f\uff0c\u800c\u59cb\u7ec8\u4e3a\u6b63\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-distancia-entre-dos-planos-paralelos\"><\/span>\u8ba1\u7b97\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u7684\u8ddd\u79bb\u603b\u662f\u76f8\u540c\uff0c\u56e0\u6b64\uff0c\u8981\u627e\u5230\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u4e24\u4e2a\u5e73\u9762\u4e4b\u4e00\u4e0a\u53d6\u4e00\u70b9\uff0c\u7136\u540e\u8ba1\u7b97\u4ece\u8be5\u70b9\u5230\u53e6\u4e00\u4e2a\u5e73\u9762\u7684\u8ddd\u79bb\u3002<\/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\/distance-entre-deux-plans-paralleles.webp\" alt=\"\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\" class=\"wp-image-2647\" width=\"401\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5b83\u662f\u4e00\u79cd\u6c42\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u8ddd\u79bb\u7684\u65b9\u6cd5\u3002\u7136\u800c\uff0c\u5f53\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\u7684\u7cfb\u6570 A\u3001B \u548c C \u91cd\u5408\u65f6\uff0c\u8fd8\u6709\u4e00\u79cd\u66f4\u7b80\u5355\u7684\u65b9\u6cd5\uff1a<\/p>\n<p>\u8003\u8651\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u7684\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\uff1a<\/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>\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u8ddd\u79bb\u7684\u8ba1\u7b97\u516c\u5f0f<\/strong>\u4e3a\uff1a<\/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>\u56e0\u6b64\uff0c\u4f7f\u7528\u516c\u5f0f\u80af\u5b9a\u66f4\u5bb9\u6613\u627e\u5230\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u56e0\u4e3a\u8fd9\u53ea\u662f\u5e94\u7528\u516c\u5f0f\u7684\u95ee\u9898\uff0c\u4ec5\u6b64\u800c\u5df2\uff0c\u4f46\u8fd9\u53d6\u51b3\u4e8e\u95ee\u9898\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8ba4\u4e3a\u6700\u597d\u89e3\u91ca\u4e24\u79cd\u8ba1\u7b97\u8ddd\u79bb\u7684\u65b9\u6cd5\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u9009\u62e9\u60a8\u559c\u6b22\u7684\u4e00\u79cd\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u8ba1\u7b97\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u793a\u4f8b<\/h3>\n<p>\u4f5c\u4e3a\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a<\/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>\u6211\u4eec\u5fc5\u987b\u9996\u5148\u9a8c\u8bc1\u6211\u4eec\u6b63\u5728\u5904\u7406\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u3002\u56e0\u6b64\uff0c\u9664\u4e86\u72ec\u7acb\u9879\u4e4b\u5916\uff0c\u5e73\u9762\u65b9\u7a0b\u7684\u6240\u6709\u7cfb\u6570\u90fd\u662f\u6210\u6bd4\u4f8b\u7684\uff0c\u56e0\u6b64\u5b83\u4eec\u5b9e\u9645\u4e0a\u662f\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u3002<\/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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\u7684 A\u3001B \u548c C \u9879\u5e76\u4e0d\u91cd\u5408\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u7b2c\u4e8c\u4e2a\u5e73\u9762\u7684\u6574\u4e2a\u65b9\u7a0b\u9664\u4ee5 2 \u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff1a<\/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>\u6240\u4ee5\uff0c\u4e24\u4e2a\u5e73\u9762\u7684\u65b9\u7a0b\u5df2\u7ecf\u5177\u6709\u76f8\u540c\u7684\u7cfb\u6570A\u3001B\u548cC\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u8f7b\u677e\u8ba1\u7b97\u51fa\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a<\/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>\u6211\u4eec\u4ee3\u5165\u6570\u503c\u5e76\u6c42\u89e3\u8fd0\u7b97\uff1a<\/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>\u4f7f\u5f97\u4e00\u4e2a\u5e73\u9762\u548c\u53e6\u4e00\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u7b49\u4e8e\u4e00\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-distancia-de-un-punto-a-un-plano\"><\/span>\u89e3\u51b3\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u70b9 P \u4e0e\u7b1b\u5361\u5c14\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u4e3a\u7684\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-80f2f62e8bfd05d8d6f6d8341c0bb0fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,0,-1) \\qquad \\qquad \\pi: \\ x-3y+2z-4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"339\" 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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u5fc5\u987b\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5404\u4e2a\u53c2\u6570\u7684\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-23e86b0b23677612b604cb66fb8d63ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 1\\cdot 2+(-3)\\cdot 0+2\\cdot (-1)-4\\rvert}{\\sqrt{1^2+(-3)^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"310\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u8fdb\u884c\u64cd\u4f5c\uff1a <\/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-e947d902a760182e4518c89dd743d9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 2+0-2-4\\rvert}{\\sqrt{1+9+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"190\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f67bf3231fbdd1e0e0be07f3252dace_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -4\\rvert}{\\sqrt{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"112\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c92e0662fecd16f52c300603444e4dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{4}}{\\bm{\\sqrt{14}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"107\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u6c42\u70b9 P \u4e0e\u5e73\u9762 \u03c0 \u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-4a3458d356f7bffc69bc0f986b1682d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,4,3) \\qquad \\qquad \\pi: \\ y=5x-2z\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" 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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u4f7f\u7528\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\u516c\u5f0f\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u5fc5\u987b\u5c06\u5e73\u9762\u8868\u8fbe\u4e3a\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\uff1a<\/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-ef28b8fe3e435d42ebba26a0644e4b5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi: \\ -5x+y+2z=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"167\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u516c\u5f0f\u6765\u786e\u5b9a\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u6bcf\u4e00\u9879\u7684\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-4b60e5f2a3865e5077f484a741ccfe2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -5\\cdot (-1)+1\\cdot 4+2\\cdot 3+0\\rvert}{\\sqrt{(-5)^2+1^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"296\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a <\/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-350cfedc4d96fd5cdd987bd3c9fbcc8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 5+4+6\\rvert}{\\sqrt{25+1+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"173\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffd92b77650ccab388d90bf6dbd365ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = }\\cfrac{\\bm{15}}{\\bm{\\sqrt{30}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"107\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4f7f\u7528\u70b9\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u6765\u786e\u5b9a\u70b9 P \u662f\u5426\u4f4d\u4e8e\u5e73\u9762 \u03c0 \u5185\u3002 <\/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-0f1172694919a2ec59e99d94477e10e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-3,5) \\qquad \\qquad \\pi: \\ 4x+6y+2z+8=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" 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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u68c0\u67e5\u8be5\u70b9\u662f\u5426\u5c5e\u4e8e\u5e73\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u4e24\u8005\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a\u5982\u679c\u8ddd\u79bb\u4e3a\u96f6\uff0c\u5219\u610f\u5473\u7740\u8be5\u70b9\u786e\u5b9e\u5c5e\u4e8e\u5e73\u9762\uff0c\u53cd\u4e4b\uff0c\u5982\u679c\u8ddd\u79bb\u4e0d\u7b49\u4e8e 0\uff0c\u5219\u610f\u5473\u7740\u8be5\u70b9\u5c5e\u4e8e\u8be5\u5e73\u9762\u3002\u70b9\u5728\u5e73\u9762\u5916\u3002\u8ba1\u5212\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u6839\u636e\u4ee5\u4e0b\u516c\u5f0f\u786e\u5b9a\u70b9\u4e0e\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fa5cd77905fa8723448de603b90b705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"300\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62c5bc20a51cc65d03c68c20f08afc11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert 4\\cdot 0+6\\cdot (-3)+2\\cdot 5+8\\rvert}{\\sqrt{4^2+6^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"282\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc797a0472cb98c5901fc294efe5988c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -18+10+8\\rvert}{\\sqrt{16+36+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"191\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7abeba148ae6b786dcdd35df00f7c308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{0}{\\sqrt{56}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"112\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36660ee3653f3f3fcd120a6016e5dd8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(P,\\pi) = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u70b9\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u7b49\u4e8e\u96f6\uff0c\u56e0\u6b64\u5b9e\u9645\u4e0a<strong>\u8be5\u70b9\u5c5e\u4e8e\u5e73\u9762\u3002<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u6c42\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-b51c64f5f5d25771ee1eb45d8e37e2f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 2x-y+5z-3=0 \\qquad \\qquad  \\pi_2 : \\ 2x-y+5z-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"453\" 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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5fc5\u987b\u9996\u5148\u9a8c\u8bc1\u6211\u4eec\u6b63\u5728\u5904\u7406\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u3002\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\u7684\u6240\u6709\u7cfb\u6570\u9664\u72ec\u7acb\u9879\u5916\u5747\u6210\u6bd4\u4f8b\uff0c\u56e0\u6b64\u8fd9\u786e\u5b9e\u662f\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u3002<\/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-4c520445614ecabfaf8a1bda841afa65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{2}=\\cfrac{-1}{-1}=\\cfrac{5}{5} \\neq \\cfrac{-3}{-7} \\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 class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u7cfb\u6570 A\u3001B \u548c C \u76f8\u7b49\uff1a<\/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 class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u516c\u5f0f\u5e76\u6267\u884c\u8fd0\u7b97\uff1a <\/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-c107ce392f40f085eadf58283ea31fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi) = \\cfrac{\\lvert -7-3\\rvert}{\\sqrt{2^2+(-1)^2+5^2}}= \\cfrac{\\lvert -10\\rvert}{\\sqrt{30}} = \\cfrac{\\bm{10}}{\\bm{\\sqrt{30}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"343\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u6c42\u4e0b\u5217\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-6d14719b0eefd313552d5257c249c66f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ \\begin{cases} x=3+4\\lambda-2 \\mu \\\\[1.7ex]y=-2+\\lambda+6 \\mu \\\\[1.7ex]z=5-\\lambda+3 \\mu \\end{cases}\\qquad \\qquad  \\pi_2 : \\ 3x+2y-2z-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"477\" style=\"vertical-align: 0px;\"><\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u524d\u666f\u5e73\u9762\u4ee5\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c\u56e0\u6b64\u8981\u5e94\u7528\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u5c06\u5176\u8f6c\u6362\u4e3a\u4e00\u822c\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u8fd9\u9700\u8981\u5927\u91cf\u7684\u8ba1\u7b97\u548c\u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5728\u8be5\u5e73\u9762\u4e0a\u53d6\u4e00\u4e2a\u70b9\u5e76\u8ba1\u7b97\u4ece\u8be5\u70b9\u5230\u53e6\u4e00\u4e2a\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u901f\u5ea6\u4f1a\u66f4\u5feb\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5e73\u9762 \u03c0 <sub>1<\/sub>\u901a\u8fc7\u7684\u70b9\u7684\u5750\u6807\u5bf9\u5e94\u4e8e\u6bcf\u4e2a\u53c2\u6570\u65b9\u7a0b\u7684\u72ec\u7acb\u9879\uff1a<\/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-d66243e674f3ead58ca1ff6b29a9a715_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5e94\u7528\u516c\u5f0f\u6765\u8ba1\u7b97\u8be5\u70b9\u4e0e\u53e6\u4e00\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-8e667bbf8e826d021b1cb466a3b312ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert A\\cdot x_0+B\\cdot y_0+C\\cdot z_0+D\\rvert}{\\sqrt{A^2+B^2+C^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"307\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4c4801629feef3733a4564df35d3c46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert 3\\cdot 3+2\\cdot (-2)+(-2)\\cdot 5-9\\rvert}{\\sqrt{3^2+2^2+(-2)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"317\" style=\"vertical-align: -20px;\"><\/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-617538033c94b7606ec4aff058302fd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert 9-4-10-9\\rvert}{\\sqrt{9+4+4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"206\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-112e5dabc19834e9cd886f6c9296452a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{\\lvert -14\\rvert}{\\sqrt{17}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"128\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18ff6ac34eed85be881c346ecb7e41dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,\\pi_2) = \\cfrac{14}{\\sqrt{17}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"119\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a\uff1a <\/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-ef887cbd7e8b9c8bbe88736ce26776d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{d(\\pi_1,\\pi_2)=d(P,\\pi_2) =} \\cfrac{\\bm{14}}{\\bm{\\sqrt{17}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"204\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u7a7a\u95f4\u4e2d\u7684\u70b9\u548c\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e7%82%b9%e5%88%b0%e5%b9%b3%e9%9d%a2%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e7%ad%94%e5%ae%9e%e4%be%8b%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u7a7a\u95f4\u4e2d\u4e00\u70b9\u5230\u5e73\u9762\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09<\/span> \u67e5\u770b\u5168\u6587 &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-246","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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