{"id":257,"date":"2023-07-10T08:01:56","date_gmt":"2023-07-10T08:01:56","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e7%ba%bf\/"},"modified":"2023-07-10T08:01:56","modified_gmt":"2023-07-10T08:01:56","slug":"%e5%85%b1%e9%9d%a2%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e7%ba%bf\/","title":{"rendered":"\u5171\u9762\u7ebf"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4e24\u6761\u7ebf\u5171\u9762\u65f6\u7684\u542b\u4e49\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u4e24\u6761\u7ebf\u4f55\u65f6\u5171\u9762\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u5171\u9762\u7ebf\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-rectas-coplanarias\"><\/span>\u4ec0\u4e48\u662f\u4e24\u6761\u5171\u9762\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u5171\u9762\u7ebf\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p><strong>\u5f53\u4e24\u6761\u76f4\u7ebf\u5728\u540c\u4e00\u5e73\u9762\u5185\u65f6\uff0c\u5b83\u4eec\u5171\u9762\u3002<\/strong>\u56e0\u6b64\uff0c\u5171\u9762\u7ebf\u53ea\u80fd\u662f<a href=\"https:\/\/mathority.org\/cn\/\u76f8\u4ea4\u7ebf\u793a\u4f8b\/\">\u5272\u7ebf<\/a>\u3001<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u884c\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50\/\">\u5e73\u884c\u7ebf<\/a>\u6216<a href=\"https:\/\/mathority.org\/cn\/\u91cd\u5408\u7ebf\u5b9a\u4e49\u548c\u793a\u4f8b\/\">\u91cd\u5408\u7ebf<\/a>\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u4e24\u6761\u5171\u9762\u7ebf\u8db3\u4ee5\u5b8c\u5168\u5b9a\u4e49\u4e00\u4e2a\u5e73\u9762\u3002\u867d\u7136\u663e\u7136\u4e00\u4e2a\u5e73\u9762\u53ef\u4ee5\u6709\u4e24\u6761\u4ee5\u4e0a\u7684\u5171\u9762\u7ebf\uff0c\u4f46\u5b9e\u9645\u4e0a\u6bcf\u4e2a\u5e73\u9762\u90fd\u5305\u542b\u65e0\u9650\u591a\u6761\u7ebf\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4e24\u6761\u7ebf\u4e0d\u5171\u9762\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u76f8\u4ea4\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-rectas-coplanarias\"><\/span>\u5171\u9762\u7ebf\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u66f4\u597d\u5730\u7406\u89e3\u5171\u9762\u7ebf\u7684\u6982\u5ff5\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u5305\u542b\u4e09\u6761\u7ebf\u7684\u793a\u4f8b\uff1a <\/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\/coplanaire-droit.webp\" alt=\"\u5171\u9762\u7ebf\u7684\u793a\u4f8b\" class=\"wp-image-3117\" width=\"344\" height=\"197\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4eec\u662f\u5171\u9762\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u5c5e\u4e8e\u540c\u4e00\u5e73\u9762\u3002\u76f8\u53cd\uff0c\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-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>\u4e0e\u5176\u4ed6\u4e24\u6761\u7ebf\u4e0d\u5171\u9762\uff0c\u56e0\u4e3a\u5b83\u4e0e\u5176\u4ed6\u4e24\u6761\u7ebf\u76f8\u4ea4<\/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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-rectas-son-coplanarias\"><\/span>\u5982\u4f55\u77e5\u9053\u4e24\u6761\u7ebf\u662f\u5426\u5171\u9762\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u5bf9\u5171\u9762\u7ebf\u7684\u89e3\u91ca\u4e2d\u770b\u5230\u7684\uff0c\u8fd9\u4e9b\u7ebf\u53ea\u80fd\u662f\u5272\u7ebf\u3001\u5e73\u884c\u7ebf\u6216\u91cd\u5408\u7ebf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e24\u6761\u4ea4\u53c9\u7ebf\u6c38\u8fdc\u4e0d\u4f1a\u5171\u9762\u3002<\/p>\n<p><strong>\u56e0\u6b64\uff0c\u8981\u77e5\u9053\u4e24\u6761\u76f4\u7ebf\u662f\u5426\u5171\u9762\uff0c\u5fc5\u987b\u786e\u5b9a\u5b83\u4eec\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u5982\u679c\u5b83\u4eec\u662f\u4e24\u6761\u76f8\u4ea4\u3001\u5e73\u884c\u6216\u91cd\u5408\u7684\u76f4\u7ebf\uff0c\u5219\u8bf4\u660e\u5b83\u4eec\u662f\u5171\u9762\u7684\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u68c0\u67e5\u4e24\u6761\u7ebf\u7684\u5171\u9762\u6027\uff0c\u9996\u5148\u5fc5\u987b\u77e5\u9053\u5982\u4f55<a href=\"https:\/\/mathority.org\/cn\/\u7a7a\u95f4\u4e2d\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e-r3-\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u8ba1\u7b97\u4e24\u6761\u7ebf\u5728\u7a7a\u95f4\u4e2d\u7684\u76f8\u5bf9\u4f4d\u7f6e<\/a>\u3002\u5982\u679c\u60a8\u4ecd\u7136\u4e0d\u719f\u6089\u8fd9\u4e2a\u6982\u5ff5\uff0c\u6700\u597d\u5148\u67e5\u770b\u94fe\u63a5\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u627e\u5230\u5b8c\u6574\u7684\u89e3\u91ca\u4ee5\u53ca\u793a\u4f8b\u3001\u7ec3\u4e60\u548c\u5df2\u89e3\u51b3\u7684\u95ee\u9898\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-rectas-coplanarias\"><\/span>\u89e3\u51b3\u4e86\u5171\u9762\u7ebf\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u5171\u9762\u7ebf\u4e0a\u7684\u5178\u578b\u7ec3\u4e60\uff1a<\/p>\n<ul>\n<li>\u5224\u65ad\u4e0b\u5217\u4e24\u6761\u76f4\u7ebf\u662f\u5426\u5171\u9762\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e57f7dd2bfa67f2cf4eb2ee0455dcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=3-2t \\\\[1.7ex] y=4t \\\\[1.7ex] z=5 \\end{cases} \\qquad \\qquad s : \\ \\begin{cases} 2x+y=0 \\\\[1.7ex] z=-2\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"345\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5fc5\u987b\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u76f8\u540c\u7c7b\u578b\u7684\u65b9\u7a0b\u6765\u8868\u8fbe\u4e24\u6761\u7ebf\u3002\u7136\u540e\u6211\u4eec\u5c06\u7a7f\u8fc7\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>\u4ece\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u5230\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-5d8dbc805cb7e0020c9c82c90e56e011_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s : \\ \\begin{cases} 2x+y=0 \\\\[1.7ex] z=-2\\end{cases}  \\xrightarrow{x \\ = \\ t} \\ \\begin{cases} 2t+y=0 \\\\[1.7ex] z=-2\\end{cases} \\longrightarrow \\ \\begin{cases} x=t \\\\[1.7ex] y=-2t \\\\[1.7ex] z=-2\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\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-c1704f760e99807be417afa3891f8db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-2,4,0) \\qquad \\qquad  \\vv{\\text{v}}_s = (1,-2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"291\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e24\u6761\u7ebf\u7684\u65b9\u5411\u77e2\u91cf\u7684\u5750\u6807\u6210\u6bd4\u4f8b\uff0c\u56e0\u6b64\u53ea\u80fd\u662f\u91cd\u5408\u7ebf\u6216\u5e73\u884c\u7ebf\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\uff0c\u4e0d\u9700\u8981\u8ba1\u7b97\u7cbe\u786e\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u56e0\u4e3a\u5e73\u884c\u7ebf\u548c\u91cd\u5408\u7ebf\u662f\u5171\u9762\u7ebf\u3002\u6240\u4ee5<strong>\u8fd9\u4e24\u6761\u7ebf\u662f\u5171\u9762\u7684<\/strong>\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4e24\u6761\u7ebf\u5171\u9762\u65f6\u7684\u542b\u4e49\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u4e24\u6761\u7ebf\u4f55\u65f6\u5171\u9762\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u5171\u9762\u7ebf\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e7%ba%bf\/\"> <span class=\"screen-reader-text\">\u5171\u9762\u7ebf<\/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-257","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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