{"id":242,"date":"2023-07-10T14:58:48","date_gmt":"2023-07-10T14:58:48","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%90%91%e9%87%8f%e6%96%b9%e7%a8%8b%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b\/"},"modified":"2023-07-10T14:58:48","modified_gmt":"2023-07-10T14:58:48","slug":"%e5%b9%b3%e9%9d%a2%e5%90%91%e9%87%8f%e6%96%b9%e7%a8%8b%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%90%91%e9%87%8f%e6%96%b9%e7%a8%8b%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b\/","title":{"rendered":"\u5e73\u9762\u7684\u5411\u91cf\u65b9\u7a0b"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\u60a8\u5c06\u627e\u5230\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\uff08\u516c\u5f0f\uff09\u548c\u8ba1\u7b97\u793a\u4f8b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7ec3\u4e60\u6765\u7ec3\u4e60\u5e76\u89e3\u51b3\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u7684\u95ee\u9898\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-es-la-ecuacion-vectorial-de-un-plano\"><\/span>\u5e73\u9762\u7684\u77e2\u91cf\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\u77e2\u91cf\u65b9\u7a0b<\/strong>\u662f\u5141\u8bb8\u4efb\u4f55\u5e73\u9762\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u7684\u65b9\u7a0b\u3002\u8981\u627e\u5230\u5e73\u9762\u7684\u5411\u91cf\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-la-ecuacion-vectorial-del-plano\"><\/span>\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<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\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-d80b8a9d79088c24cb1940b2abeb18bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" 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-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 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>\u56e0\u6b64\uff0c\u8fd9\u610f\u5473\u7740\u5e73\u9762\u4e0a\u7684\u4efb\u4f55\u70b9\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a 1 \u4e2a\u70b9\u548c 2 \u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\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\u7684\u5728\u7ebf\u5411\u91cf\u65b9\u7a0b\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8fdb\u4e00\u6b65\u5730\uff0c\u4e0a\u5f0f\u5bf9\u5e94\u4e00\u4e2a\u5e73\u9762\u7684\u5fc5\u8981\u6761\u4ef6\u662f\u8be5\u5e73\u9762\u7684\u4e24\u4e2a\u5411\u91cf\u5177\u6709\u7ebf\u6027\u72ec\u7acb\u6027\uff0c\u5373\u4e24\u4e2a\u5411\u91cf\u4e0d\u80fd\u4e92\u76f8\u5e73\u884c\u3002\u5176\u4ed6\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u9664\u4e86\u77e2\u91cf\u65b9\u7a0b\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\u53ef\u4ee5\u89e3\u6790\u5730\u8868\u8fbe\u5e73\u9762\uff0c\u4f8b\u5982<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u9762\u53c2\u6570\u65b9\u7a0b\/\">\u5e73\u9762\u7684\u53c2\u6570\u65b9\u7a0b<\/a>\u548c<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u9762\u7684\u9690\u5f0f\u4e00\u822c\u65b9\u7a0b\u6216\u7b1b\u5361\u5c14\u65b9\u7a0b\/\">\u5e73\u9762\u7684\u9690\u5f0f\u65b9\u7a0b<\/a>\u3002\u60a8\u53ef\u4ee5\u5728\u94fe\u63a5\u4e2d\u68c0\u67e5\u6bcf\u79cd\u7c7b\u578b\u7684\u65b9\u7a0b\u662f\u4ec0\u4e48\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-ecuacion-vectorial-de-un-plano\"><\/span>\u5982\u4f55\u6c42\u5e73\u9762\u77e2\u91cf\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>\u770b\u5b8c\u4e86\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u6982\u5ff5\u7684\u89e3\u91ca\uff0c\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\u77e2\u91cf\u65b9\u7a0b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66c1bcf32c114fa640cf6c3291ec42ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,0,4)\" 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-742e72027d137839ae3e565d098418f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(1,3,-2)\" 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-85abe8a10ab167a3b72ce2048d480c5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(5,0,1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p>\u8981\u786e\u5b9a\u5e73\u9762\u7684\u77e2\u91cf\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-d80b8a9d79088c24cb1940b2abeb18bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u70b9\u548c\u6bcf\u4e2a\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-e966b1b217e19b857d5945de152312cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x,y,z)=(2,0,4)+\\lambda (1,3,-2) + \\mu (5,0,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u5728\u793a\u4f8b\u4e2d\u6240\u770b\u5230\u7684\uff0c\u627e\u5230\u5e73\u9762\u7684\u77e2\u91cf\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-la-ecuacion-vectorial-del-plano\"><\/span>\u5e73\u9762\u5411\u91cf\u65b9\u7a0b\u6c42\u89e3\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\u5411\u91cf\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-967feca863a9a4d3f1e7f0267f5e75e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(0,-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-b080bdb2f119700090341574b7bbf489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,3,-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-3ad5d13132fc818eac77b60b1ac15e13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(2,-1,5).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-b85ba6303c469618bd0d69f560c11535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-1,5) - (1,3,-1) = (1,-4,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u5e73\u9762\u548c\u70b9\u7684\u4e24\u4e2a\u65b9\u5411\u5411\u91cf\uff0c\u56e0\u6b64\u6211\u4eec\u4f7f\u7528\u5e73\u9762\u5411\u91cf\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-d80b8a9d79088c24cb1940b2abeb18bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" style=\"vertical-align: -5px;\"><\/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-941c8d43b51f4c2f838a0ef55b1f87fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x,y,z)=(1,3,-1)+\\lambda (0,-2,3) + \\mu (1,-4,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" style=\"vertical-align: -5px;\"><\/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\u77e2\u91cf\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-c61c59f12a57c3df9dcd45d35e601a65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,-2,1) \\qquad B(1,0,4) \\qquad C(-1,3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"322\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u5e73\u9762\u7684\u5411\u91cf\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u4e24\u4e2a\u5728\u5e73\u9762\u4e0a\u7ed3\u5408\u7684\u7ebf\u6027\u65e0\u5173\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-fabb606f5950c8b864f9c2e67b4ba576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (1,0,4) - (2,-2,1) = (-1,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-1a4d8bb247e7d07e78d9db6229d7bb5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (-1,3,-2) - (2,-2,1) = (-3,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" 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\u56e0\u6b64\u6211\u4eec\u5e94\u7528\u5e73\u9762\u5411\u91cf\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-d80b8a9d79088c24cb1940b2abeb18bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{\\text{u}} + \\mu \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" style=\"vertical-align: -5px;\"><\/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-baa213bb98612c8fff5d3830141936a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x,y,z)=(2,-2,1)+\\lambda (-1,2,3) + \\mu (-3,5,-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"368\" style=\"vertical-align: -5px;\"><\/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\u7a7a\u95f4\u4e2d\u5c5e\u4e8e\u7531\u4ee5\u4e0b\u5411\u91cf\u65b9\u7a0b\u5b9a\u4e49\u7684\u5e73\u9762\u7684 4 \u4e2a\u70b9\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f741afbd4a2497d23e451858c85f24c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,2,1)+\\lambda (2,-1,4) + \\mu (-1,3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"340\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u5e73\u9762\u4e0a\u7684\u70b9\uff0c\u53ea\u9700\u4e3a\u53c2\u6570\u6307\u5b9a\u4efb\u610f\u503c\u5373\u53ef<\/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-f057d6a413d6aaa2ff88a679887b506d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u7136\u800c\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-132014e2e535396ec5fbd90f506d9d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\lambda =0 \\\\[2ex] \\mu =0 \\end{array} \\right\\} \\longrightarrow \\ (0,2,1)+0\\cdot (2,-1,4) + 0\\cdot  (-1,3,0)= \\bm{(0,2,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"473\" 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-203c86c8c4e062be8c995bec8c3cfbd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\lambda =1 \\\\[2ex] \\mu =0 \\end{array} \\right\\} \\longrightarrow \\ (0,2,1)+1\\cdot (2,-1,4) + 0\\cdot (-1,3,0)= \\bm{(2,1,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"473\" 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-6f4a371c0ec352adf59ee80a81086982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\lambda =0 \\\\[2ex] \\mu =1 \\end{array} \\right\\} \\longrightarrow \\ (0,2,1)+0\\cdot (2,-1,4) + 1\\cdot (-1,3,0)= \\bm{(-1,5,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"487\" 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-38353c40eec5b104be40c3e0a0c93d04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} \\lambda =1 \\\\[2ex] \\mu =1 \\end{array} \\right\\} \\longrightarrow \\ (0,2,1)+1\\cdot (2,-1,4) + 1\\cdot (-1,3,0)= \\bm{(1,4,5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"473\" 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\u77e2\u91cf\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-5b06057454aa6047223c595fdb8d60f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=4+2t \\\\[1.7ex] y=-1+t\\\\[1.7ex] z=5-4t \\end{cases} \\qquad \\qquad s: \\ \\frac{x-1}{2} = \\frac{y+2}{4}= \\frac{z+1}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"429\" 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\u77e2\u91cf\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u4e24\u4e2a\u65b9\u5411\u77e2\u91cf\u548c\u8be5\u5e73\u9762\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-9e313a8b4e84e6b176488218f026cc17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(2,1,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u540c\u4e00\u76f4\u7ebf\u4e0a\u4e00\u70b9\u7684\u7b1b\u5361\u5c14\u5750\u6807\u662f\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-610ad4575988feaea1215caf1913b014_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(4,-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-5fa0ec21ddcb8da0da4286a89b6e2232_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} =(2,4,-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\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-f4e01864a3c82e5d4eec6142ac295d11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=P+\\lambda \\vv{r} + \\mu \\vv{s}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"176\" 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-a3f612d981cb579e43104dc679b36bc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x,y,z)=(4,-1,5)+\\lambda (2,1,-4) + \\mu (2,4,-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-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\u60a8\u5c06\u627e\u5230\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\uff08\u516c\u5f0f\uff09\u548c\u8ba1\u7b97\u793a\u4f8b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7ec3\u4e60\u6765\u7ec3\u4e60\u5e76\u89e3\u51b3\u5e73\u9762\u77e2\u91cf\u65b9\u7a0b\u7684\u95ee\u9898\u3002 \u5e73\u9762 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%b9%b3%e9%9d%a2%e5%90%91%e9%87%8f%e6%96%b9%e7%a8%8b%e5%85%ac%e5%bc%8f%e7%a4%ba%e4%be%8b\/\"> <span class=\"screen-reader-text\">\u5e73\u9762\u7684\u5411\u91cf\u65b9\u7a0b<\/span> \u67e5\u770b\u5168\u6587 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