{"id":243,"date":"2023-07-10T14:29:46","date_gmt":"2023-07-10T14:29:46","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/"},"modified":"2023-07-10T14:29:46","modified_gmt":"2023-07-10T14:29:46","slug":"%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/","title":{"rendered":"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u4eec\u7684\u8ba1\u7b97\u65b9\u5f0f\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%bfque-son-las-ecuaciones-parametricas-de-un-plano\"><\/span>\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\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>\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b<\/strong>\u662f\u5141\u8bb8\u4efb\u4f55\u5e73\u9762\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u7684\u65b9\u7a0b\u3002\u4e3a\u4e86\u627e\u5230\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\uff0c\u6211\u4eec\u53ea\u9700\u8981\u4e00\u4e2a\u70b9\u548c\u5c5e\u4e8e\u8be5\u5e73\u9762\u7684\u4e24\u4e2a\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-las-ecuaciones-parametricas-del-plano\"><\/span>\u89c4\u5212\u53c2\u6570\u65b9\u7a0b\u7684\u5236\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\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 style=\"text-align:left\"><strong>\u5e73\u9762\u53c2\u6570\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-3f74da212d3f5f1c3a3002d71a4bed96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex]  y=P_y + \\lambda  \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;\">\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<\/div>\n<p>\u91cd\u8981\u7684\u662f\u5e73\u9762\u65b9\u7a0b\u7684\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u5177\u6709\u4e0d\u540c\uff08\u4e0d\u5e73\u884c\uff09\u7684\u65b9\u5411\u3002\u5426\u5219\uff0c\u4e0a\u9762\u7684\u7b49\u5f0f\u5c31\u4ee3\u8868\u6ca1\u6709\u8ba1\u5212\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=\"\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u9664\u4e86\u53c2\u6570\u65b9\u7a0b\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\u53ef\u4ee5\u89e3\u6790\u5730\u8868\u8fbe\u7a7a\u95f4\u4e2d\u7684\u5e73\u9762\uff08\u5728 R3 \u4e2d\uff09\uff0c\u4f8b\u5982<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u9762\u7684\u9690\u5f0f\u4e00\u822c\u65b9\u7a0b\u6216\u7b1b\u5361\u5c14\u65b9\u7a0b\/\">\u4e00\u822c\u5e73\u9762\u65b9\u7a0b<\/a>\u3002\u5728\u6b64\u94fe\u63a5\u4e2d\uff0c\u60a8\u5c06\u627e\u5230\u5b83\u7684\u516c\u5f0f\u3001\u5982\u4f55\u6839\u636e\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\u8ba1\u7b97\u5b83\u3001\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-las-ecuaciones-parametricas-de-un-plano\"><\/span>\u5982\u4f55\u6c42\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\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>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1a<\/p>\n<ul>\n<li>\u6c42\u901a\u8fc7\u8be5\u70b9\u7684\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3f0118e7d45cb9daa5eb13da519c4c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5e76\u5305\u542b\u5411\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-181eea061c4ba593347d9a9418e929f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(2,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/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-1902a5430dccdf4883ac68065ccaad61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(4,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p>\u8981\u786e\u5b9a\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\uff0c\u53ea\u9700\u5e94\u7528\u5176\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-46f87775f11f01a59c70aa3ee864aebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u70b9\u548c\u6bcf\u4e2a\u65b9\u5411\u5411\u91cf\u4ee3\u5165\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-501ec8b26b4d88ebe95abd3ca7e7fe44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=1 + \\lambda \\cdot 2 + \\mu \\cdot 4 \\\\[1.7ex] y=3+ \\lambda \\cdot 0 + \\mu \\cdot 2\\\\[1.7ex] z=2 + \\lambda\\cdot (-1)+ \\mu \\cdot 3\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e8517084217ee5519c428b598f2d7f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=1 + 2\\lambda + 4\\mu } \\\\[1.7ex] \\bm{y=3 + 2\\mu}\\\\[1.7ex] \\bm{z=2 -\\lambda+ 3\\mu} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-pasar-de-la-ecuacion-vectorial-de-un-plano-a-ecuaciones-parametricas\"><\/span>\u5982\u4f55\u4ece\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u8f6c\u4e3a\u53c2\u6570\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u786e\u5b9a\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u6839\u636e\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u3002\u4e0b\u9762\u4f60\u53ef\u4ee5\u770b\u5230\u6f14\u793a\u3002<\/p>\n<p>\u8bbe\u4efb\u610f\u5e73\u9762\u7684\u77e2\u91cf\u65b9\u7a0b\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-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>\u6211\u4eec\u9996\u5148\u8fdb\u884c\u5411\u91cf\u4e0e\u6807\u91cf\u7684\u4e58\u79ef\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-9eb7c00ddf8ba235e3698c85a0f23db0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+ (\\lambda\\text{u}_x,\\lambda\\text{u}_y,\\lambda\\text{u}_z) +(\\mu\\text{v}_x,\\mu\\text{v}_y,\\mu\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"440\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6dfb\u52a0\u7ec4\u4ef6\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-e3ff52d13a3d4400800b0f72148f99c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x+\\lambda \\text{u}_x + \\mu \\text{v}_x,P_y+\\lambda \\text{u}_y + \\mu \\text{v}_y,P_z+\\lambda \\text{u}_z + \\mu \\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"467\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u901a\u8fc7\u5206\u522b\u540c\u5316\u6bcf\u4e2a\u53d8\u91cf\u5bf9\u5e94\u7684\u5750\u6807\uff0c\u5f97\u5230\u5e73\u9762\u7684\u53c2\u6570\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-46f87775f11f01a59c70aa3ee864aebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u5728\u4e0a\u9762\u7684\u4e24\u4e2a\u793a\u4f8b\u4e2d\u6240\u770b\u5230\u7684\uff0c\u627e\u5230\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\u76f8\u5bf9\u5bb9\u6613\u3002\u7136\u800c\uff0c\u95ee\u9898\u53ef\u80fd\u4f1a\u53d8\u5f97\u6709\u70b9\u590d\u6742\uff0c\u6240\u4ee5\u4e0b\u9762\u6709\u51e0\u4e2a\u4e0d\u540c\u96be\u5ea6\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-ecuaciones-parametricas-del-plano\"><\/span>\u89e3\u51b3\u4e86\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u5305\u542b\u5411\u91cf\u7684\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b<\/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-490c9a9e1ad20441fc3e4e552562da06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(2,1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5e76\u7ecf\u8fc7\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0c8787181ac89109302dca999a33418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/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-6b15174216dceaaf397f378acb645116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(-2,-1,1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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\u77e5\u9053\u5e73\u9762\u7684\u65b9\u7a0b\uff0c\u60a8\u9700\u8981\u4e00\u4e2a\u70b9\u548c\u4e24\u4e2a\u5411\u91cf\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u53ea\u6709\u4e00\u4e2a\u5411\u91cf\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u627e\u5230\u8be5\u5e73\u9762\u7684\u53e6\u4e00\u4e2a\u5b9a\u5411\u5411\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5b9a\u4e49\u5e73\u9762\u4e24\u70b9\u7684\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-42b4f718ed5e9e490fb0129949f8f694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (-2,-1,1) - (3,2,-1) = (-5,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u5e73\u9762\u548c\u70b9\u7684\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\uff0c\u56e0\u6b64\u6211\u4eec\u4f7f\u7528\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\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-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u8fd9\u4e24\u4e2a\u5411\u91cf\u548c\u5e73\u9762\u4e0a\u7684\u4e24\u70b9\u4e4b\u4e00\u4ee3\u5165\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-ecedfca92c24d2754bcca977f2f30e76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=3 + \\lambda \\cdot 2+ \\mu \\cdot (-5) \\\\[1.7ex] y=2 + \\lambda \\cdot 1 + \\mu \\cdot (-3) \\\\[1.7ex] z=(-1) + \\lambda\\cdot 5 + \\mu \\cdot 2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c67219e6157433f05d410c0aefb05f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=3 +2 \\lambda-5\\mu } \\\\[1.7ex] \\bm{y=2 + \\lambda-3 \\mu } \\\\[1.7ex] \\bm{z=-1 + 5\\lambda + 2\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"151\" style=\"vertical-align: 0px;\"><\/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\u5305\u542b\u4ee5\u4e0b\u4e09\u70b9\u7684\u5e73\u9762\u7684\u53c2\u6570\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-df564519d92ccbe87c5500460231d2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,1,0) \\qquad B(2,-3,-1) \\qquad C(1,5,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" 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\u627e\u5230\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u5728\u5e73\u9762\u4e2d\u94fe\u63a5\u7684\u4e24\u4e2a\u7ebf\u6027\u72ec\u7acb\u5411\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u7531 3 \u4e2a\u70b9\u5b9a\u4e49\u7684\u4e24\u4e2a\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-14d7f4f29cbdc14a69357bf1b8f29b4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-3,-1) - (4,1,0) = (-2,-4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" 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-0a33c0974226c3e3c0a51de22c0b8b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (1,5,3) - (4,1,0) = (-3,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u627e\u5230\u7684\u4e24\u4e2a\u5411\u91cf\u7684\u5750\u6807\u4e0d\u6210\u6bd4\u4f8b\uff0c\u56e0\u6b64\u5b83\u4eec\u5f7c\u6b64\u7ebf\u6027\u65e0\u5173\u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\u548c\u5e73\u9762\u4e0a\u7684\u4e00\u4e2a\u70b9\uff0c\u6211\u4eec\u5e94\u7528\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\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-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u8fd9\u4e24\u4e2a\u5411\u91cf\u548c\u5e73\u9762\u4e0a\u7684\u4e09\u4e2a\u70b9\u4e4b\u4e00\u4ee3\u5165\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-f57edaf8a85108cffb796470ffca8484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=4 + \\lambda \\cdot (-2)+ \\mu \\cdot (-3) \\\\[1.7ex] y=1 + \\lambda \\cdot (-4) + \\mu \\cdot 4 \\\\[1.7ex] z=0 + \\lambda\\cdot (-1) + \\mu \\cdot 3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"218\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cab5ddc074bd7df6849d71854207cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=4 -2 \\lambda-3\\mu } \\\\[1.7ex] \\bm{y=1-4 \\lambda+4 \\mu } \\\\[1.7ex] \\bm{z=-\\lambda + 3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"138\" style=\"vertical-align: 0px;\"><\/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>\u8ba1\u7b97\u7531\u4ee5\u4e0b\u77e2\u91cf\u65b9\u7a0b\u5b9a\u4e49\u7684\u5e73\u9762\u7684\u53c2\u6570\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-01df6ae373f0d460332985a54715ca88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+\\lambda (6,1,-2) + \\mu (1,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" 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\u5c06\u5e73\u9762\u7684\u77e2\u91cf\u65b9\u7a0b\u8f6c\u6362\u4e3a\u53c2\u6570\u65b9\u7a0b\uff0c\u5fc5\u987b\u5bf9\u5750\u6807\u8fdb\u884c\u8fd0\u7b97\uff0c\u7136\u540e\u5206\u522b\u6c42\u89e3\u6bcf\u4e2a\u53d8\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-01df6ae373f0d460332985a54715ca88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+\\lambda (6,1,-2) + \\mu (1,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" 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-0b2bc3ea152efd43fbb9a16f7d1c73b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+(6\\lambda,\\lambda,-2\\lambda) + (\\mu,-\\mu,3\\mu)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8760242bbd8cf85b3d2e7280e1c0a2e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(6\\lambda+\\mu,-1+\\lambda-\\mu,5-2\\lambda+3\\mu)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"339\" 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-381b1ceea87f332904ae69a566ecd1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=6\\lambda+\\mu } \\\\[1.7ex] \\bm{y=-1+\\lambda-\\mu} \\\\[1.7ex] \\bm{z=5-2\\lambda+3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/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\u5305\u542b\u76f4\u7ebf\u7684\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b<\/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>\u5e76\u4e14\u4e0e\u53f3\u8fb9\u5e73\u884c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u884c\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-624f315685b292c4bb05e9cb4b931a97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=1+t \\\\[1.7ex] y=2-3t\\\\[1.7ex] z=4+2t \\end{cases} \\qquad \\qquad s: \\ \\frac{x-4}{2} = \\frac{y+3}{2}= \\frac{z-2}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"424\" 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\">\u4e3a\u4e86\u627e\u5230\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\u548c\u5e73\u9762\u4e0a\u7684\u4e00\u4e2a\u70b9\u3002\u8be5\u6307\u4ee4\u544a\u8bc9\u6211\u4eec\u5b83\u5305\u542b\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>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u65b9\u5411\u5411\u91cf\u548c\u8fd9\u6761\u7ebf\u4e0a\u7684\u4e00\u70b9\u6765\u5b9a\u4e49\u5e73\u9762\u3002\u6b64\u5916\uff0c\u8be5\u9648\u8ff0\u544a\u8bc9\u6211\u4eec\u8be5\u5e73\u9762\u5e73\u884c\u4e8e\u76f4\u7ebf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cc36ef269909ae645021a09d5e91016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528\u8fd9\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u6765\u8868\u793a\u5e73\u9762\u65b9\u7a0b\u3002<\/p>\n<p class=\"has-text-align-left\">\u6b63\u786e\u7684<\/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>\u4ee5\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u56e0\u6b64\u5176\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u5c31\u662f\u53c2\u6570\u9879\u7684\u7cfb\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b40bdea86f773b36fb40078fb4ddf23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(1,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u540c\u4e00\u6761\u7ebf\u4e0a\u7684\u70b9\u7684\u7b1b\u5361\u5c14\u5750\u6807\u662f\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-d565383a925076ae118032f7b9b62f7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u76f4\u7ebf<\/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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u5176\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u662f\u5206\u6570\u7684\u5206\u6bcd\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-a8f571b217df7a6bbe833d706091457a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} =(2,2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u89c4\u5212\u7684\u53c2\u6570\u65b9\u7a0b\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-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c81f4d8e5aa907f111b3389d5137736e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=1 + \\lambda \\cdot 1+ \\mu \\cdot 2 \\\\[1.7ex] y=2 + \\lambda \\cdot (-3) + \\mu \\cdot 2 \\\\[1.7ex] z=4 + \\lambda\\cdot 2 + \\mu \\cdot (-3) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"189\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fccd86ac9a3e4084e324d8e5b1071e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=1 + \\lambda+2\\mu } \\\\[1.7ex] \\bm{y=2-3 \\lambda+2 \\mu } \\\\[1.7ex] \\bm{z=4+2\\lambda -3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/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\u627e\u5230\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u4eec\u7684\u8ba1\u7b97\u65b9\u5f0f\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 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\"> <span class=\"screen-reader-text\">\u5e73\u9762\u53c2\u6570\u65b9\u7a0b<\/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-243","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\u53c2\u6570\u65b9\u7a0b - 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\u53c2\u6570\u65b9\u7a0b\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b - Mathority\" \/>\n<meta property=\"og:description\" content=\"\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u4eec\u7684\u8ba1\u7b97\u65b9\u5f0f\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 &hellip; \u5e73\u9762\u53c2\u6570\u65b9\u7a0b \u67e5\u770b\u5168\u6587 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/cn\/\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T14:29:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" \/>\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%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\"},\"author\":{\"name\":\"Mathority\u56e2\u961f\",\"@id\":\"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071\"},\"headline\":\"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\",\"datePublished\":\"2023-07-10T14:29:46+00:00\",\"dateModified\":\"2023-07-10T14:29:46+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\"},\"wordCount\":1,\"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%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\",\"url\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\",\"name\":\"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/cn\/#website\"},\"datePublished\":\"2023-07-10T14:29:46+00:00\",\"dateModified\":\"2023-07-10T14:29:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/cn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\"}]},{\"@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\u53c2\u6570\u65b9\u7a0b - 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\u53c2\u6570\u65b9\u7a0b\/","og_locale":"zh_CN","og_type":"article","og_title":"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b - Mathority","og_description":"\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u8ba1\u5212\u7684\u53c2\u6570\u65b9\u7a0b\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u4eec\u7684\u8ba1\u7b97\u65b9\u5f0f\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 &hellip; \u5e73\u9762\u53c2\u6570\u65b9\u7a0b \u67e5\u770b\u5168\u6587 &raquo;","og_url":"https:\/\/mathority.org\/cn\/\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\/","article_published_time":"2023-07-10T14:29:46+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png"}],"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%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/"},"author":{"name":"Mathority\u56e2\u961f","@id":"https:\/\/mathority.org\/cn\/#\/schema\/person\/7f15c6882833e0b2765bbb87c6ce3071"},"headline":"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b","datePublished":"2023-07-10T14:29:46+00:00","dateModified":"2023-07-10T14:29:46+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/"},"wordCount":1,"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%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/","url":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/","name":"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/cn\/#website"},"datePublished":"2023-07-10T14:29:46+00:00","dateModified":"2023-07-10T14:29:46+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/cn\/"},{"@type":"ListItem","position":2,"name":"\u5e73\u9762\u53c2\u6570\u65b9\u7a0b"}]},{"@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\/243","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=243"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/posts\/243\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/media?parent=243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/categories?post=243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/cn\/wp-json\/wp\/v2\/tags?post=243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}