{"id":265,"date":"2023-07-10T04:04:14","date_gmt":"2023-07-10T04:04:14","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/"},"modified":"2023-07-10T04:04:14","modified_gmt":"2023-07-10T04:04:14","slug":"%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/","title":{"rendered":"\u5e73\u9762\uff08\u51e0\u4f55\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5173\u4e8e\u5e73\u9762\u662f\u4ec0\u4e48\u3001\u5e73\u9762\u7684\u8ba1\u7b97\u65b9\u5f0f\u53ca\u5176\u6240\u6709\u5c5e\u6027\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5e73\u9762\u7684\u793a\u4f8b\u3001\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u662f\u4ec0\u4e48\u3001\u5982\u4f55\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u4ee5\u53ca\u6700\u540e\u5982\u4f55\u4f7f\u7528\u5e73\u9762\u65b9\u7a0b\u4ee5\u6570\u5b57\u65b9\u5f0f\u8868\u8fbe\u4efb\u4f55\u5e73\u9762\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-plano\"><\/span>\u4ec0\u4e48\u662f\u8ba1\u5212\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u5e73\u9762\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p><strong>\u5e73\u9762\u662f\u5177\u6709\u4e24\u4e2a\u7ef4\u5ea6\uff08\u957f\u5ea6\u548c\u5bbd\u5ea6\uff09\u7684\u51e0\u4f55\u5bf9\u8c61\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\/quel-est-l-avion.webp\" alt=\"\u4ec0\u4e48\u662f\u7b1b\u5361\u5c14\u5e73\u9762\" class=\"wp-image-3433\" width=\"417\" height=\"203\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u5e73\u9762\u5305\u542b\u65e0\u9650\u591a\u6761\u7ebf\u548c\u65e0\u9650\u591a\u70b9\u3002\u5728\u4e0a\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u5e73\u9762\u3001\u76f4\u7ebf\u548c\u70b9\u4e4b\u95f4\u7684\u533a\u522b\u3002\u60a8\u8fd8\u53ef\u4ee5\u9a8c\u8bc1\u8be5\u884c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u5c0f\u8d39<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5305\u542b\u5728\u98de\u673a\u5185<\/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>\u6b63\u5982\u60a8\u5728\u56fe\u8868\u8ba1\u5212\u4e2d\u770b\u5230\u7684\uff0c\u8ba1\u5212\u901a\u5e38\u4ee5\u5e0c\u814a\u5b57\u6bcd\u547d\u540d\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-fdef793ea5450647d6139c80d45be77a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi, \\alpha, \\beta,...\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"71\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5728\u6570\u5b66\u4e2d\u7ecf\u5e38\u4f7f\u7528\u7684\u5e73\u9762\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\u7b1b\u5361\u5c14\u5e73\u9762\u3002\u7b1b\u5361\u5c14\u5e73\u9762\u662f\u7531\u6a2a\u5750\u6807\u8f74\uff08X\u8f74\uff09\u548c\u7eb5\u5750\u6807\u8f74\uff08Y\u8f74\uff09\u5b9a\u4e49\u7684\u5e73\u9762\u3002\u7b1b\u5361\u5c14\u5e73\u9762\u7684\u7528\u9014\u4e4b\u4e00\u662f\u5b83\u7528\u4e8e\u63cf\u8ff0\u53c2\u8003\u7cfb\u4e2d\u5bf9\u8c61\u7684\u4f4d\u7f6e\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinacion-de-un-plano\"><\/span>\u786e\u5b9a\u8ba1\u5212<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u5e73\u9762\u7684\u542b\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u786e\u5b9a\u4e09\u7ef4\u7a7a\u95f4\uff08R3 \u4e2d\uff09\u4e2d\u7684\u4efb\u610f\u5e73\u9762\u3002<\/p>\n<p>\u8ba1\u5212\u5b8c\u5168\u7531\u4ee5\u4e0b\u51e0\u4f55\u5143\u7d20\u51b3\u5b9a\uff1a<\/p>\n<ul>\n<li>\u4e09\u70b9\u672a\u5bf9\u9f50\u3002<\/li>\n<li>\u4e00\u6761\u76f4\u7ebf\u548c\u4e00\u4e2a\u70b9\u5728\u5916\u9762\u3002<\/li>\n<li>\u4e24\u6761\u5e73\u884c\u7ebf\u6216\u4e24\u6761\u76f8\u4ea4\u7ebf\u3002<\/li>\n<\/ul>\n<p>\u5173\u4e8e\u6700\u540e\u4e00\u70b9\uff0c\u60a8\u53ef\u80fd\u5df2\u7ecf\u77e5\u9053\u4e24\u6761\u7ebf\u5e73\u884c\u610f\u5473\u7740\u4ec0\u4e48\u3002\u4f46\u5272\u7ebf\u7684\u542b\u4e49\u5374\u9c9c\u4e3a\u4eba\u77e5\uff0c\u6240\u4ee5\u5982\u679c\u60a8\u5728\u8fd9\u91cc\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u53ef\u4ee5\u67e5\u770b<a href=\"https:\/\/mathority.org\/cn\/\u76f8\u4ea4\u7ebf\u793a\u4f8b\/\">\u4ec0\u4e48\u662f\u5272\u7ebf<\/a>\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5177\u5907\u4e86\u524d\u97623\u4e2a\u6761\u4ef6\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\uff0c\u5c31\u8bf4\u660e\u6211\u4eec\u53ef\u4ee5\u5236\u5b9a\u8ba1\u5212\u4e86\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-plano\"><\/span>\u8ba1\u5212\u8d22\u4ea7<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8be5\u8ba1\u5212\u6ee1\u8db3\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u4e00\u4e2a\u5e73\u9762\u5305\u542b\u65e0\u6570\u4e2a\u70b9\u3002<\/li>\n<li>\u4e00\u4e2a\u5e73\u9762\u5305\u542b\u65e0\u6570\u6761\u76f4\u7ebf\u3002<\/li>\n<li>\u5e73\u9762\u662f\u65e0\u9650\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u662f\u5728\u7a7a\u95f4\u4e2d\u65e0\u9650\u5ef6\u4f38\u7684\u8868\u9762\u3002<\/li>\n<li>\u4e24\u4e2a\u76f8\u4ea4\u7684\u5e73\u9762\u786e\u5b9a\u4e00\u6761\u7ebf\u3002<\/li>\n<li>\u5728\u5e73\u9762\u4e0a\u6709\u4e00\u70b9\u7684\u7ebf\u4e0d\u4e00\u5b9a\u5305\u542b\u5728\u5e73\u9762\u4e0a\u3002\u8981\u4f7f\u4e00\u6761\u7ebf\u6210\u4e3a\u5e73\u9762\u7684\u4e00\u90e8\u5206\uff0c\u5b83\u5fc5\u987b\u5728\u5e73\u9762\u4e0a\u81f3\u5c11\u6709\u4e24\u4e2a\u70b9\u3002<\/li>\n<li>\u65e0\u9650\u4e2a\u5e73\u9762\u4e0e\u76f4\u7ebf\u76f8\u4ea4\u3002<\/li>\n<li>\u534a\u5e73\u9762\u662f\u5e73\u9762\u88ab\u5176\u4e2d\u4e00\u6761\u7ebf\u5207\u5272\u65f6\u5206\u6210\u7684\u4e24\u4e2a\u90e8\u5206\u4e2d\u7684\u6bcf\u4e00\u4e2a\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-del-plano\"><\/span>\u5e73\u9762\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c<strong>\u5e73\u9762\u65b9\u7a0b<\/strong>\u662f\u5141\u8bb8\u4efb\u4f55\u5e73\u9762\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u7684\u65b9\u7a0b\u3002\u56e0\u6b64\uff0c\u8981\u627e\u5230\u5e73\u9762\u7684\u65b9\u7a0b\uff0c\u60a8\u53ea\u9700\u8981\u4e00\u4e2a\u70b9\u548c\u5c5e\u4e8e\u8be5\u5e73\u9762\u7684\u4e24\u4e2a\u7ebf\u6027\u65e0\u5173\u5411\u91cf\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\/equations-planes.webp\" alt=\"xy\u5e73\u9762\u65b9\u7a0b\u5728\u7ebf\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u7136\u800c\uff0c\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u5bf9\u8ba1\u5212\u6982\u5ff5\u7684\u89e3\u91ca\u4e2d\u6240\u770b\u5230\u7684\uff0c\u786e\u5b9a\u8ba1\u5212\u7684\u65b9\u6cd5\u6709\u591a\u79cd\u3002\u90a3\u4e48\uff0c\u540c\u6837\u5730\uff0c\u5206\u6790\u6027\u5730\u8868\u8fbe\u8ba1\u5212\u4e5f\u6709\u4e0d\u540c\u7684\u65b9\u5f0f\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6240\u6709\u7c7b\u578b\u7684\u5e73\u9762\u65b9\u7a0b\u4e3a\uff1a<strong>\u77e2\u91cf\u65b9\u7a0b<\/strong>\u3001<strong>\u53c2\u6570\u65b9\u7a0b<\/strong>\u3001<strong>\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b<\/strong>\u548c<strong>\u5e73\u9762\u7684\u6b63\u5219\uff08\u6216\u5206\u6bb5\uff09\u65b9\u7a0b<\/strong>\u3002<\/p>\n<p>\u7136\u540e\u6211\u4eec\u5c06\u8be6\u7ec6\u770b\u5230\u8be5\u8ba1\u5212\u6240\u6709\u65b9\u7a0b\u7684\u89e3\u91ca\u548c\u516c\u5f0f\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-vectorial-del-plano\"><\/span>\u5e73\u9762\u7684\u5411\u91cf\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8003\u8651\u5e73\u9762\u7684\u4e00\u4e2a\u70b9\u548c\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\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-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><strong>\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u7684\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-d9227901692832cb0c176a896d35e896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      (x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6216\u540c\u7b49\u5b66\u5386\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-78b41d21b63c22ec05d3f93576a897e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+\\lambda (\\text{u}_x,\\text{u}_y,\\text{u}_z) + \\mu (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"398\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u4e24\u4e2a\u6807\u91cf\uff0c\u4e5f\u5c31\u662f\u8bf4\u4e24\u4e2a\u5b9e\u6570\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-parametricas-del-plano\"><\/span>\u5e73\u9762\u53c2\u6570\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\u7684<\/strong>\u516c\u5f0f\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-e1791802331aa9973126b3d7c7f1b716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u4e24\u4e2a\u6807\u91cf\uff0c\u4e5f\u5c31\u662f\u8bf4\u4e24\u4e2a\u5b9e\u6570\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b77e9af6839a6bc60da39dd1798dd6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{u}_x,\\text{u}_y,\\text{u}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -6px;\"><\/p>\n<p>\u662f\u8ba1\u5212\u7684\u4e24\u4e2a\u5f15\u5bfc\u5411\u91cf\u4e4b\u4e00\u7684\u5206\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8a3eef2109d6a80a337c88337a1443e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -6px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f61b32275ccdbca7f8d5e0b3c750dd35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_x,\\text{v}_y,\\text{v}_z\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -6px;\"><\/p>\n<p>\u662f\u8ba1\u5212\u7684\u53e6\u4e00\u4e2a\u5b9a\u5411\u5411\u91cf\u7684\u7ec4\u6210\u90e8\u5206<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75c6a57a037206319f16dec389993ded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z).\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -6px;\"><\/p>\n<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-implicita-o-general-del-plano\"><\/span>\u5e73\u9762\u7684\u9690\u5f0f\u6216\u4e00\u822c\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8003\u8651\u5e73\u9762\u7684\u4e00\u4e2a\u70b9\u548c\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\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-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>\u5e73\u9762\u7684\u9690\u5f0f\u3001\u4e00\u822c\u6216\u7b1b\u5361\u5c14\u65b9\u7a0b\u901a\u8fc7\u6c42\u89e3\u4ee5\u4e0b\u884c\u5217\u5f0f\u5e76\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0 \u6765\u83b7\u5f97\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-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>\u56e0\u6b64\uff0c<strong>\u6240\u5f97\u8ba1\u5212\u7684\u9690\u5f0f\u6216\u4e00\u822c\u65b9\u7a0b<\/strong>\u5982\u4e0b\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-7dcacf16123986ecd33dace4f4411914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle Ax+By+Cz+D=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b64\u7c7b\u5e73\u9762\u65b9\u7a0b\u4e5f\u79f0\u4e3a\u7b1b\u5361\u5c14\u5e73\u9762\u65b9\u7a0b\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-o-segmentaria-del-plano\"><\/span>\u5e73\u9762\u7684\u6b63\u5219\u65b9\u7a0b\u6216\u5206\u6bb5\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5e73\u9762\u7684\u6b63\u5219\u6216\u5206\u6bb5\u65b9\u7a0b\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\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-7c19853d465a703aa398bde04fa3222c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\cfrac{x}{a}+\\cfrac{y}{b} + \\cfrac{z}{c} = 1  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5e73\u9762\u4e0e X \u8f74\u7684\u4ea4\u70b9\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5e73\u9762\u4e0e Y \u8f74\u7684\u4ea4\u70b9\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd9\u662f\u5e73\u9762\u4e0e Z \u8f74\u76f8\u4ea4\u7684\u4f4d\u7f6e\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<p>\u5e73\u9762\u7684\u6b63\u5219\u65b9\u7a0b\uff08\u6216\u5206\u6bb5\u65b9\u7a0b\uff09\u4e5f\u53ef\u4ee5\u7531\u5176\u4e00\u822c\u65b9\u7a0b\u5f97\u5230\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-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>\u9996\u5148\uff0c\u6211\u4eec\u4ece\u65b9\u7a0b\u4e2d\u6c42\u89e3\u7cfb\u6570 D\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-7e6829185741f883a29bf004cbf570a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+Cz=-D\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"166\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\u6211\u4eec\u5c06\u8ba1\u5212\u7684\u6574\u4e2a\u65b9\u7a0b\u9664\u4ee5\u53c2\u6570 D \u6539\u53d8\u7b26\u53f7\u7684\u503c\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-04843e22b4176c0ce921483f93dffeab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax+By+Cz}{-D}=\\cfrac{-D}{-D}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"176\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-278ce62f85ca44612254f48e96154726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{Ax}{-D}+\\cfrac{By}{-D}+\\cfrac{Cz}{-D}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"166\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5e76\u4e14\uff0c\u5229\u7528\u5206\u6570\u7684\u6027\u8d28\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u8868\u8fbe\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-a58254e773c7c14b5b337a4330997125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{-\\frac{D}{A}}+\\cfrac{y}{-\\frac{D}{A}}+\\cfrac{z}{-\\frac{D}{A}}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"167\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u4ece\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u63a8\u5bfc\u51fa\u5141\u8bb8\u76f4\u63a5\u8ba1\u7b97\u5e73\u9762\u7684\u6b63\u5219\u6216\u5206\u6bb5\u65b9\u7a0b\u7684\u9879\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-86975df14352b1b0c2ca05d2daaf40f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=-\\cfrac{D}{A} \\qquad b=-\\cfrac{D}{B} \\qquad c=-\\cfrac{D}{C}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"260\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u80fd\u591f\u5f62\u6210\u8be5\u8ba1\u5212\u65b9\u7a0b\u7684\u53d8\u4f53\uff0c\u7cfb\u6570 A\u3001B \u548c C \u5fc5\u987b\u4e0d\u4e3a\u96f6\uff0c\u4ece\u800c\u907f\u514d\u5206\u6570\u7684\u4e0d\u786e\u5b9a\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"posicion-relativa-de-dos-planos\"><\/span>\u4e24\u4e2a\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u53ea\u6709\u4e09\u79cd\u53ef\u80fd\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff1a\u5272\u5e73\u9762\u3001\u5e73\u884c\u5e73\u9762\u548c\u91cd\u5408\u5e73\u9762\u3002<\/p>\n<ul>\n<li><strong>\u76f8\u4ea4\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u4ec5\u76f8\u4ea4\u4e8e\u4e00\u6761\u76f4\u7ebf\uff0c\u5219\u4e24\u4e2a\u5e73\u9762\u76f8\u4ea4\u3002<\/li>\n<li><strong>\u5e73\u884c\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u5728\u4efb\u4f55\u4e00\u70b9\u90fd\u4e0d\u76f8\u4ea4\uff0c\u5219\u5b83\u4eec\u5e73\u884c\u3002<\/li>\n<li><strong>\u91cd\u5408\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u90fd\u6709\u516c\u5171\u70b9\uff0c\u5219\u4e24\u4e2a\u5e73\u9762\u91cd\u5408\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-30\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u76f8\u4ea4\u5e73\u9762<\/strong><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-secants.webp\" alt=\"\u4e24\u4e2a\u76f8\u4ea4\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2814\" width=\"265\" height=\"258\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u5e73\u884c\u5e73\u9762<\/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=\"\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2815\" width=\"266\" height=\"166\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u91cd\u5408\u5e73\u9762<\/strong><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/deux-avions-coincidents.webp\" alt=\"\u4e24\u4e2a\u91cd\u5408\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2820\" width=\"294\" height=\"83\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<p>\u53e6\u5916\uff0c\u5982\u679c\u4e24\u4e2a\u76f8\u4ea4\u5e73\u9762\u4ee5 90\u00b0 \u89d2\u76f8\u4ea4\uff0c\u5219\u5b83\u4eec\u662f\u4e24\u4e2a<strong>\u76f8\u4e92\u5782\u76f4\u7684\u5e73\u9762<\/strong>\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"angulo-entre-dos-planos\"><\/span> \u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7b49\u4e8e\u6240\u8ff0\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u5f62\u6210\u7684\u89d2\u5ea6\u3002\u56e0\u6b64\uff0c<strong>\u4e3a\u4e86\u627e\u5230\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u9700\u8981\u8ba1\u7b97\u5b83\u4eec\u7684\u6cd5\u5411\u91cf\u5f62\u6210\u7684\u89d2\u5ea6\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u76f8\u7b49\u7684\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c\u4e00\u65e6\u6211\u4eec\u786e\u5207\u5730\u77e5\u9053\u4e86\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7531\u4ec0\u4e48\u7ec4\u6210\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u770b\u770b\u8ba1\u7b97\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u516c\u5f0f\uff0c\u8be5\u516c\u5f0f\u662f\u4ece\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u516c\u5f0f\u63a8\u5bfc\u51fa\u6765\u7684\uff1a<\/p>\n<p>\u7ed9\u5b9a\u4e24\u4e2a\u4e0d\u540c\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-dfa3d7e6f1ece8353327be7c9227d75b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ A_1x+B_1y+C_1z+D_1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c3966346685421fe3e535cf57a5491d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A_2x+B_2y+C_2z+D_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6bcf\u4e2a\u5e73\u9762\u7684\u6cd5\u5411\u91cf\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-eb0ca06882e0d61d6f8134368946ef29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1=(A_1,B_1,C_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22fba6a063a544bdf257e64d8d139238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2=(A_2,B_2,C_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8fd9\u4e24\u4e2a\u5e73\u9762\u5f62\u6210\u7684\u89d2\u5ea6\u662f\u901a\u8fc7\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u5b83\u4eec\u7684\u6cd5\u5411\u91cf\u5f62\u6210\u7684\u89d2\u5ea6\u6765\u786e\u5b9a\u7684\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-a0329572a30e8d75bd3795469fe65493_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{n}_1 \\cdot \\vv{n}_2\\rvert}{\\lvert \\vv{n}_1 \\rvert \\cdot \\lvert \\vv{n}_2 \\rvert} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u663e\u7136\uff0c\u4e00\u65e6\u6211\u4eec\u6839\u636e\u516c\u5f0f\u8ba1\u7b97\u51fa\u4e86\u4e24\u4e2a\u5e73\u9762\u6240\u6210\u89d2\u5ea6\u7684\u4f59\u5f26\uff0c\u5c31\u5fc5\u987b\u5c06\u4f59\u5f26\u53cd\u8f6c\u624d\u80fd\u627e\u5230\u8be5\u89d2\u5ea6\u7684\u503c\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u4e24\u4e2a\u5e73\u9762\u5782\u76f4\u6216\u5e73\u884c\u65f6\uff0c\u5219\u4e0d\u5fc5\u5e94\u7528\u8be5\u516c\u5f0f\uff0c\u56e0\u4e3a\u53ef\u4ee5\u76f4\u63a5\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\uff1a<\/p>\n<ul>\n<li>\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u4e3a 0\u00b0\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u6cd5\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u3002<\/li>\n<li>\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u4e3a 90\u00b0\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u6cd5\u5411\u91cf\u4e5f\u5f7c\u6b64\u5782\u76f4\uff08\u6216\u6b63\u4ea4\uff09\uff0c\u56e0\u6b64\u5f62\u6210\u76f4\u89d2\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5173\u4e8e\u5e73\u9762\u662f\u4ec0\u4e48\u3001\u5e73\u9762\u7684\u8ba1\u7b97\u65b9\u5f0f\u53ca\u5176\u6240\u6709\u5c5e\u6027\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5e73\u9762\u7684\u793a\u4f8b\u3001\u4e24\u4e2a\u5e73\u9762\u4e4b &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\"> <span class=\"screen-reader-text\">\u5e73\u9762\uff08\u51e0\u4f55\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-265","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>\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority<\/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\/cn\/\u5e73\u9762\u51e0\u4f55\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority\" \/>\n<meta property=\"og:description\" content=\"\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5173\u4e8e\u5e73\u9762\u662f\u4ec0\u4e48\u3001\u5e73\u9762\u7684\u8ba1\u7b97\u65b9\u5f0f\u53ca\u5176\u6240\u6709\u5c5e\u6027\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5e73\u9762\u7684\u793a\u4f8b\u3001\u4e24\u4e2a\u5e73\u9762\u4e4b &hellip; \u5e73\u9762\uff08\u51e0\u4f55\uff09 \u67e5\u770b\u5168\u6587 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/cn\/\u5e73\u9762\u51e0\u4f55\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T04:04:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quel-est-l-avion.webp\" \/>\n<meta name=\"author\" content=\"Mathority\u56e2\u961f\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority\u56e2\u961f\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\"},\"author\":{\"name\":\"Mathority\u56e2\u961f\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071\"},\"headline\":\"\u5e73\u9762\uff08\u51e0\u4f55\uff09\",\"datePublished\":\"2023-07-10T04:04:14+00:00\",\"dateModified\":\"2023-07-10T04:04:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\"},\"wordCount\":11,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/cn\/#organization\"},\"articleSection\":[\"\u70b9\u3001\u7ebf\u3001\u9762\"],\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\",\"url\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\",\"name\":\"\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/#website\"},\"datePublished\":\"2023-07-10T04:04:14+00:00\",\"dateModified\":\"2023-07-10T04:04:14+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/cn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u5e73\u9762\uff08\u51e0\u4f55\uff09\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/cn\/#website\",\"url\":\"https:\/\/mathority.org\/cn\/\",\"name\":\"Mathority\",\"description\":\"\u597d\u5947\u5fc3\u4e0e\u8ba1\u7b97\u7684\u7ed3\u5408\uff01\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/cn\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/cn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/cn\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/cn\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071\",\"name\":\"Mathority\u56e2\u961f\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"caption\":\"Mathority\u56e2\u961f\"},\"sameAs\":[\"http:\/\/mathority.org\/cn\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/cn\/\u5e73\u9762\u51e0\u4f55\/","og_locale":"zh_CN","og_type":"article","og_title":"\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority","og_description":"\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5173\u4e8e\u5e73\u9762\u662f\u4ec0\u4e48\u3001\u5e73\u9762\u7684\u8ba1\u7b97\u65b9\u5f0f\u53ca\u5176\u6240\u6709\u5c5e\u6027\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5e73\u9762\u7684\u793a\u4f8b\u3001\u4e24\u4e2a\u5e73\u9762\u4e4b &hellip; \u5e73\u9762\uff08\u51e0\u4f55\uff09 \u67e5\u770b\u5168\u6587 &raquo;","og_url":"https:\/\/mathority.org\/cn\/\u5e73\u9762\u51e0\u4f55\/","article_published_time":"2023-07-10T04:04:14+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quel-est-l-avion.webp"}],"author":"Mathority\u56e2\u961f","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"Mathority\u56e2\u961f"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/"},"author":{"name":"Mathority\u56e2\u961f","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071"},"headline":"\u5e73\u9762\uff08\u51e0\u4f55\uff09","datePublished":"2023-07-10T04:04:14+00:00","dateModified":"2023-07-10T04:04:14+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/"},"wordCount":11,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/cn\/#organization"},"articleSection":["\u70b9\u3001\u7ebf\u3001\u9762"],"inLanguage":"zh-Hans","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/","url":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/","name":"\u5e73\u9762\uff08\u51e0\u4f55\uff09 - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/#website"},"datePublished":"2023-07-10T04:04:14+00:00","dateModified":"2023-07-10T04:04:14+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%87%a0%e4%bd%95\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/cn\/"},{"@type":"ListItem","position":2,"name":"\u5e73\u9762\uff08\u51e0\u4f55\uff09"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/cn\/#website","url":"https:\/\/mathority.org\/cn\/","name":"Mathority","description":"\u597d\u5947\u5fc3\u4e0e\u8ba1\u7b97\u7684\u7ed3\u5408\uff01","publisher":{"@id":"https:\/\/mathority.org\/cn\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/cn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Organization","@id":"https:\/\/mathority.org\/cn\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/cn\/","logo":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/cn\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/cn\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071","name":"Mathority\u56e2\u961f","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","caption":"Mathority\u56e2\u961f"},"sameAs":["http:\/\/mathority.org\/cn"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts\/265","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/comments?post=265"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts\/265\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/media?parent=265"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/categories?post=265"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/tags?post=265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}