{"id":247,"date":"2023-07-10T12:56:19","date_gmt":"2023-07-10T12:56:19","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%ba%bf%e7%9a%84%e7%9b%b8%e5%af%b9%e4%bd%8d%e7%bd%ae-r3-%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T12:56:19","modified_gmt":"2023-07-10T12:56:19","slug":"%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%ba%bf%e7%9a%84%e7%9b%b8%e5%af%b9%e4%bd%8d%e7%bd%ae-r3-%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%ba%bf%e7%9a%84%e7%9b%b8%e5%af%b9%e4%bd%8d%e7%bd%ae-r3-%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u4e24\u6761\u7ebf\u5728\u7a7a\u95f4\u4e2d\u7684\u76f8\u5bf9\u4f4d\u7f6e"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u7a7a\u95f4\u4e2d\u4e24\u6761\u7ebf\u7684\u6240\u6709\u76f8\u5bf9\u4f4d\u7f6e\uff08\u5728 R3 \u4e2d\uff09\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u89e3\u91ca\u4e86\u5982\u4f55\u4f7f\u7528\u4e24\u79cd\u53ef\u80fd\u7684\u65b9\u6cd5\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff1a\u901a\u8fc7\u8303\u56f4\u6216\u4ece\u6bcf\u6761\u7ebf\u7684\u70b9\u548c\u5411\u91cf\u3002\u60a8\u751a\u81f3\u53ef\u4ee5\u770b\u5230\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\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%bfcuales-son-las-posiciones-relativas-de-dos-rectas-en-el-espacio\"><\/span>\u4e24\u6761\u7ebf\u5728\u7a7a\u95f4\u4e2d\u7684\u76f8\u5bf9\u4f4d\u7f6e\u662f\u591a\u5c11\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u5f53\u5728\u4e09\u7ef4\u7a7a\u95f4\uff08\u5728 R3 \u4e2d\uff09\u4e2d\u5de5\u4f5c\u65f6\uff0c\u4e24\u6761\u7ebf\u4e4b\u95f4\u6709 4 \u79cd\u53ef\u80fd\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff1a\u4e24\u6761\u7ebf\u53ef\u4ee5\u662f<strong>\u5408\u5e76\u7ebf<\/strong>\u3001<strong>\u5e73\u884c\u7ebf<\/strong>\u3001<strong>\u5272\u7ebf<\/strong>\u6216<strong>\u5272\u7ebf<\/strong>\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-79\">\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\u7ebf<\/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\/droites-paralleles-a-langle.webp\" alt=\"\u4e24\u6761\u5e73\u884c\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-1643\" width=\"222\" height=\"200\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u4e24\u6761\u7ebf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u4f46\u6ca1\u6709\u516c\u5171\u70b9\uff0c\u5219\u5b83\u4eec\u662f\u5e73\u884c\u7684\u3002\u6b64\u5916\uff0c\u5e73\u884c\u7ebf\u5f7c\u6b64\u4e4b\u95f4\u7684\u8ddd\u79bb\u59cb\u7ec8\u76f8\u540c\u3002 <\/p>\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\u7ebf<\/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\/angle-coincident-lignes.webp\" alt=\"\u4e24\u6761\u91cd\u5408\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-1646\" width=\"202\" height=\"179\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5982\u679c\u4e24\u6761\u7ebf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u5e76\u4e14\u5b83\u4eec\u7684\u6240\u6709\u70b9\u90fd\u662f\u516c\u5171\u7684\uff0c\u5219\u5b83\u4eec\u91cd\u5408\u3002 <\/p>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div class=\"wp-block-columns is-layout-flex wp-container-82\">\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\u7ebf<\/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\/angles-droits-secants.webp\" alt=\"\u4e24\u6761\u76f8\u4ea4\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-1644\" width=\"222\" height=\"208\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4e24\u6761\u76f8\u4ea4\u7ebf\u65b9\u5411\u4e0d\u540c\uff0c\u4f46\u4ea4\u4e8e\u4e00\u70b9\u3002 <\/p>\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>\u4ea4\u53c9\u7ebf<\/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\/lignes-dintersection-1.webp\" alt=\"\" class=\"wp-image-2692\" width=\"228\" height=\"221\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4e24\u6761\u76f8\u4ea4\u7ebf\u7684\u65b9\u5411\u4e0d\u540c\uff0c\u5e76\u4e14\u5728\u4efb\u4f55\u4e00\u70b9\u90fd\u4e0d\u76f8\u4ea4\u3002\u56e0\u6b64\uff0c\u4e24\u6761\u4ea4\u53c9\u7ebf\u4e0d\u5728\u540c\u4e00\u5e73\u9762\u4e0a\u3002\u4f8b\u5982\uff0c\u5728\u7ebf\u4e0a\u65b9\u7684\u56fe\u5f62\u8868\u793a\u4e2d<\/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>\u603b\u662f\u8d70\u5728\u524d\u9762<\/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>\uff0c\u6240\u4ee5\u4ed6\u4eec\u6c38\u8fdc\u4e0d\u4f1a\u4e92\u76f8\u63a5\u89e6\u3002<\/p>\n<\/div>\n<\/div>\n<p>\u6709\u4e24\u79cd\u65b9\u6cd5\u53ef\u4ee5\u77e5\u9053\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u56e0\u4e3a\u5b83\u4eec\u53d6\u51b3\u4e8e\u4e24\u6761\u7ebf\u7684\u65b9\u7a0b\u7684\u8868\u8fbe\u65b9\u5f0f\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u7ebf\u662f\u77e2\u91cf\u3001\u53c2\u6570\u6216\u8fde\u7eed\u65b9\u7a0b\u5f62\u5f0f\uff0c\u6700\u597d<strong>\u4ece\u6bcf\u6761\u7ebf\u7684\u4e00\u4e2a\u70b9\u548c\u4e00\u4e2a\u77e2\u91cf\u8ba1\u7b97\u76f8\u5bf9\u4f4d\u7f6e<\/strong>\uff08\u4e0b\u9762\u7ed9\u51fa\u6b64\u65b9\u6cd5\u7684\u89e3\u91ca\uff09\u3002<\/li>\n<li>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u7ebf\u4ee5\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\uff0c<strong>\u5219\u901a\u8fc7\u8ba1\u7b97\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\u66f4\u5bb9\u6613\u77e5\u9053\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e<\/strong>\uff08\u53c2\u89c1\u4e0b\u9762\u7684\u89e3\u91ca\uff09\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-la-posicion-relativa-de-dos-rectas-a-partir-de-un-punto-y-un-vector\"><\/span>\u786e\u5b9a\u70b9\u548c\u5411\u91cf\u7684\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e<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>\u60a8\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u70b9\u548c\u6bcf\u6761\u7ebf\u7684\u5411\u91cf\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u5f53\u76f4\u7ebf\u4ee5\u77e2\u91cf\u65b9\u7a0b\u3001\u53c2\u6570\u65b9\u7a0b\u6216\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\u65f6\uff0c\u9002\u5408\u4f7f\u7528\u6b64\u65b9\u6cd5\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8bbe\u65b9\u5411\u5411\u91cf\u548c\u4e24\u6761\u7ebf\u4e0a\u7684\u4efb\u610f\u70b9\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-1bdc3a31a3a5a8aa3da312bb2badb356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{v}} = (\\text{v}}_x, \\text{v}}_y,\\text{v}}_z})\\\\[2ex] P(P_x,P_y,P_z)\\end{cases} \\qquad\\qquad s: \\ \\begin{cases} \\vv{\\text{v}}' = (\\text{v}}_x', \\text{v}}_y',\\text{v}}_z'})\\\\[2ex] P'(P_x',P_y',P_z')\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"66\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u627e\u5230\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u6211\u4eec\u9700\u8981\u9075\u5faa\u4ee5\u4e0b\u8fc7\u7a0b\uff1a<\/p>\n<p> <strong><span style=\"color:#ff6f00;\">\u2023<\/span><\/strong>\u6211\u4eec\u9700\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u67e5\u770b\u4e24\u6761\u7ebf\u7684\u5411\u91cf\u662f\u5426\u6210\u6bd4\u4f8b\uff0c\u5e76\u4e14\u6839\u636e\u60c5\u51b5\uff0c\u6211\u4eec\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a<\/p>\n<ul style=\"color:#ff6f00; font-weight: bold;list-style-type:disc\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u6210\u6bd4\u4f8b\uff0c\u5219\u4e24\u6761\u7ebf\u53ef\u4ee5\u5e73\u884c\u6216\u91cd\u5408\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u68c0\u67e5\u4e00\u6761\u76f4\u7ebf\u7684\u70b9\u662f\u5426\u6ee1\u8db3\u53e6\u4e00\u6761\u76f4\u7ebf\u7684\u65b9\u7a0b\uff1a<\/span>\n<ul style=\"list-style-type:circle\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u4e00\u6761\u76f4\u7ebf\u7684\u70b9\u6ee1\u8db3\u53e6\u4e00\u6761\u76f4\u7ebf\u7684\u65b9\u7a0b\uff0c\u5219\u610f\u5473\u7740\u4e24\u6761\u76f4\u7ebf\u91cd\u5408\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u5426\u5219\uff0c\u8fd9\u610f\u5473\u7740\u4e24\u6761\u7ebf\u662f\u5e73\u884c\u7684\u3002<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u4e0d\u6210\u6bd4\u4f8b\uff0c\u5219\u76f4\u7ebf\u53ef\u80fd\u76f8\u4ea4\u6216\u76f8\u4ea4\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5fc5\u987b\u6c42\u89e3\u4ee5\u4e0b 3\u00d73 \u884c\u5217\u5f0f\uff1a<\/span>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-84a440053c71b2d4287cf246ff1d2f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\text{v}}_x &amp; \\text{v}}_x' &amp; P_x-P_x' \\\\[1.1ex] \\text{v}}_y &amp; \\text{v}}_y' &amp; P_y-P_y' \\\\[1.1ex]\\text{v}}_z &amp; \\text{v}}_z' &amp; P_z-P_z'  \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\"list-style-type:circle\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u524d\u4e00\u4e2a\u884c\u5217\u5f0f\u7b49\u4e8e 0\uff0c\u5219\u4e24\u6761\u7ebf\u76f8\u4ea4\u4e8e\u4e00\u70b9\uff08\u5b83\u4eec\u76f8\u4ea4\uff09\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u524d\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff0c\u5219\u4e24\u6761\u7ebf\u76f8\u4ea4\u3002<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u4e0b\u56fe\u603b\u7ed3\u4e86\u6574\u4e2a\u8fc7\u7a0b\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\/positions-relatives-de-deux-lignes.webp\" alt=\"\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2731\" width=\"827\" height=\"544\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-determinar-la-posicion-relativa-entre-dos-rectas\"><\/span>\u786e\u5b9a\u4e24\u6761\u7ebf\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u524d\u9762\u7684\u8fc7\u7a0b\u53ef\u80fd\u770b\u8d77\u6765\u6709\u70b9\u590d\u6742\uff0c\u4f46\u662f\u4f60\u53ef\u4ee5\u770b\u5230\u5b83\u662f\u76f8\u53cd\u7684\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u4e00\u4e2a\u95ee\u9898\u4f5c\u4e3a\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u786e\u5b9a\u4ee5\u4e0b\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-16d9c8120b44ee56adb7cd6358b34f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ (x,y,z)=(2,0,1)+t(4,-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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-0d49353d91f4eb7753b4cb7229859f81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\ (x,y,z)=(1,-3,1)+t(1,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5c06\u4e24\u6761\u76f4\u7ebf\u8868\u793a\u4e3a\u5411\u91cf\u65b9\u7a0b\uff0c\u5176\u4e2d\u6bcf\u6761\u76f4\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-c5e74a2aac28c26437e62531f2bb7c88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(4,-1,1) \\qquad \\qquad \\vv{s}=(1,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"260\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6bcf\u6761\u7ebf\u7ecf\u8fc7\u7684\u70b9\u662f\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-e9386dff14919cdeaf57a882471de177_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R(2,0,1)\\qquad \\qquad S(1,-3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u4e00\u4e2a\u70b9\u548c\u6bcf\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u5e94\u7528\u4e0a\u9762\u7684\u65b9\u6cd5\u3002\u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u68c0\u67e5\u5411\u91cf\u7684\u5750\u6807\u662f\u5426\u6210\u6bd4\u4f8b\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-fe839d3477334c9358279b3d97bcf4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{1} \\neq \\cfrac{-1}{2} \\neq \\cfrac{1}{0} \\quad \\longrightarrow \\quad \\text{No proporcionales}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"314\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u4e24\u4e2a\u5411\u91cf\u4e0d\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u7ebf\u53ea\u80fd\u76f8\u4e92\u63a5\u89e6\u6216\u4ea4\u53c9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u73b0\u5728\u9700\u8981\u6c42\u89e3\u7531\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u70b9\u5f62\u6210\u7684\u4ee5\u4e0b\u884c\u5217\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-225a68c152f54a250471b7c4c2254b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\text{v}}_x &amp; \\text{v}}_x' &amp; P_x-P_x' \\\\[1.1ex] \\text{v}}_y &amp; \\text{v}}_y' &amp; P_y-P_y' \\\\[1.1ex]\\text{v}}_z &amp; \\text{v}}_z' &amp; P_z-P_z' \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fac3bc2228451f94261e296aeecb5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 4 &amp; 1 &amp; 2-1 \\\\[1.1ex] -1 &amp; 2 &amp; 0-(-3) \\\\[1.1ex]1&amp; 0 &amp; 1-1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8ba1\u7b97\u884c\u5217\u5f0f\uff0c\u4e3a\u6b64\u60a8\u53ef\u4ee5\u4f7f\u7528\u4efb\u4f55\u65b9\u6cd5\uff08Sarrus \u89c4\u5219\u3001\u8865\u96c6\u6cd5\u6216\u8f85\u56e0\u5b50\u6cd5\u7b49\uff09\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-538af230a8105fceefc5a30f41237ea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 4 &amp; 1 &amp; 1 \\\\[1.1ex] -1 &amp; 2 &amp; 3 \\\\[1.1ex]1&amp; 0 &amp; 0 \\end{vmatrix} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u786e\u5b9a\u7684\u7ed3\u679c\u4e3a\u96f6\uff0c\u5219\u8fd9\u610f\u5473\u7740\u7ebf\u4ea4\u53c9\uff08\u5b83\u4eec\u63a5\u89e6\uff09\u3002\u4f46\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e 0\uff0c\u56e0\u6b64<strong>\u4e24\u6761\u7ebf\u76f8\u4ea4<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-la-posicion-relativa-de-dos-rectas-por-rangos\"><\/span>\u6309\u884c\u67e5\u627e\u4e24\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u627e\u5230\u4e24\u884c\u76f8\u5bf9\u4f4d\u7f6e\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u8ba1\u7b97\u4e24\u4e2a\u5177\u4f53\u77e9\u9635\u7684\u79e9\uff0c\u6211\u4eec\u5c06\u5728\u63a5\u4e0b\u6765\u770b\u5230\u3002\u5f53\u4e24\u6761\u76f4\u7ebf\u4e3a\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u5f62\u5f0f\u65f6\uff0c\u6b64\u65b9\u6cd5\u975e\u5e38\u6709\u7528\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6709\u4e24\u6761\u7ebf\u7528\u4e09\u7ef4\u7a7a\u95f4\uff08\u5728 R3 \u4e2d\uff09\u4e2d\u7684\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u8868\u793a\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-500405383e97627c17d01023fd9dd198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}A_1x+B_1y+C_1z+D_1=0 \\\\[2ex] A_2x+B_2y+C_2z+D_2=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"256\" 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-1c96b6990dae5ce476ee55689cf4f4fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ \\begin{cases}A_3x+B_3y+C_3z+D_3=0 \\\\[2ex] A_4x+B_4y+C_4z+D_4=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"256\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8bbe A \u4e3a\u4e24\u6761\u7ebf\u7684\u7cfb\u6570\u7ec4\u6210\u7684\u77e9\u9635\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-9199790c5f157691d9307604f25fc873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix}A_1 &amp; B_1 &amp; C_1\\\\[1.1ex]A_2 &amp; B_2 &amp; C_2\\\\[1.1ex]A_3 &amp; B_3 &amp; C_3\\\\[1.1ex]A_4 &amp; B_4 &amp; C_4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"158\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5e76\u7ed9\u51fa\u6269\u5c55\u77e9\u9635A&#8217;\uff0c\u5b83\u662f\u4e24\u6761\u7ebf\u7684\u6240\u6709\u53c2\u6570\u5f62\u6210\u7684\u77e9\u9635\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-f087aea2d9209341c2acf240eab2bc77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A'=\\begin{pmatrix}A_1 &amp; B_1 &amp; C_1&amp;D_1\\\\[1.1ex]A_2 &amp; B_2 &amp; C_2&amp;D_2\\\\[1.1ex]A_3 &amp; B_3 &amp; C_3&amp;D_3\\\\[1.1ex]A_4 &amp; B_4 &amp; C_4&amp;D_4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"201\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\uff0c\u6839\u636e\u524d\u4e24\u4e2a\u77e9\u9635\u7684\u8303\u56f4\uff0c\u53ef\u4ee5\u6839\u636e\u4e0b\u8868\u786e\u5b9a\u4e24\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e\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\/positions-relatives-de-deux-lignes-par-plages.webp\" alt=\"\u4e24\u884c\u6309\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2752\" width=\"494\" height=\"223\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p><strong>\u56e0\u6b64\uff0c\u4e3a\u4e86\u627e\u5230\u4e24\u884c\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\uff0c\u5e76\u4e14\u6839\u636e\u6bcf\u4e2a\u77e9\u9635\u7684\u79e9\uff0c\u8fd9\u5c06\u662f\u4e00\u79cd\u60c5\u51b5\u6216\u53e6\u4e00\u79cd\u60c5\u51b5\u3002<\/strong><\/p>\n<p>\u8fd9\u4e2a\u5b9a\u7406\u53ef\u4ee5\u4f7f\u7528 Rouch\u00e9-Frobenius \u5b9a\u7406\uff08\u4e00\u79cd\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\uff09\u6765\u8bc1\u660e\uff0c\u4f46\u662f\u5728\u672c\u9875\u4e2d\u6211\u4eec\u4e0d\u4f1a\u8fdb\u884c\u8bc1\u660e\uff0c\u56e0\u4e3a\u5b83\u76f8\u5f53\u9ebb\u70e6\u5e76\u4e14\u6ca1\u6709\u589e\u52a0\u592a\u591a\u5185\u5bb9\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-posicion-relativa-de-dos-rectas-por-rangos\"><\/span>\u5982\u4f55\u6309\u8303\u56f4\u67e5\u627e\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u4e24\u884c\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u7406\u8bba\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u770b\u770b\u5b83\u662f\u5982\u4f55\u4ed8\u8bf8\u5b9e\u8df5\u7684\uff1a<\/p>\n<ul>\n<li>\u627e\u51fa\u4ee5\u4e0b\u4e24\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-0d930886e4afd4cd3b14f1bd788c6da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}3x+2y+z+4=0 \\\\[2ex] 4x+2z+2=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"198\" 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-7704e8cf4de26fa0c249eaabdefa4150_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ \\begin{cases}3x+4z-1=0 \\\\[2ex] x-5y-2z-2=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"197\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e24\u6761\u7ebf\u662f\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u79e9\u7684\u65b9\u6cd5\u6765\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u5404\u884c\u7684\u7cfb\u6570\u6784\u9020\u77e9\u9635 A \u548c\u6269\u5c55\u77e9\u9635 A&#8217;\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-3726bfaa82678d1fffdbae281882572a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix}3 &amp; 2 &amp; 1\\\\[1.1ex]4 &amp; 0 &amp; 2\\\\[1.1ex]3 &amp; 0 &amp; 4\\\\[1.1ex]1 &amp; -5 &amp; -2 \\end{pmatrix} \\qquad \\qquad A'=\\begin{pmatrix}3 &amp; 2 &amp; 1&amp;4\\\\[1.1ex]4 &amp; 0 &amp; 2&amp;2\\\\[1.1ex]3 &amp; 0 &amp; 4&amp;-1\\\\[1.1ex]1 &amp; -5 &amp; -2 &amp;-2  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"422\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u6709\u4e86\u4e24\u4e2a\u77e9\u9635\uff0c\u6211\u4eec\u5c31\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u6211\u4eec\u9996\u5148\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635 A \u7684\u79e9\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-18eb85dd3870c1e7c865705200cf6414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-1e643845acc44a30e16f7628e85955d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}3 &amp; 2 &amp; 1\\\\[1.1ex]4 &amp; 0 &amp; 2\\\\[1.1ex]3 &amp; 0 &amp; 4 \\end{vmatrix}  = -20 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"152\" 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-466d66279a42e8aeb422d568e1547ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u77e9\u9635 A \u5305\u542b\u975e\u96f6 3\u00d73 \u5b50\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 3<\/strong> \u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u6269\u5c55\u77e9\u9635A&#8217;\u7684\u8303\u56f4\u3002\u77e9\u9635 A&#8217; \u59cb\u7ec8\u81f3\u5c11\u5904\u4e8e\u77e9\u9635 A \u7684\u79e9\uff0c\u5728\u672c\u4f8b\u4e2d\u5176\u503c\u4e3a 3\uff0c\u56e0\u6b64\u68c0\u67e5\u5b83\u662f\u79e9 4 \u8fd8\u662f\u79e9 3 \u5c31\u8db3\u591f\u4e86\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u6c42\u89e3\u884c\u5217\u5f0f4\u00d7 \u77e9\u9635 4 \u7684\u52a0\u6cd5\uff08\u6216\u8f85\u56e0\u5b50\uff09\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-d97c98cb8c416b0ce39b18628124923c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-dd21ed058cb7405e6aee811315086225_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle det(A')=\\begin{vmatrix}3 &amp; 2 &amp; 1&amp;4\\\\[1.1ex]4 &amp; 0 &amp; 2&amp;2\\\\[1.1ex]3 &amp; 0 &amp; 4&amp;-1\\\\[1.1ex]1 &amp; -5 &amp; -2 &amp;-2 \\end{vmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"234\" 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-0f99f68649b9ca6274e4531a1d172315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =3 \\cdot\\begin{vmatrix} 0 &amp; 2&amp;2\\\\[1.1ex] 0 &amp; 4&amp;-1\\\\[1.1ex] -5 &amp; -2 &amp;-2 \\end{vmatrix}-2\\cdot\\begin{vmatrix}4 &amp; 2&amp;2\\\\[1.1ex]3 &amp; 4&amp;-1\\\\[1.1ex]1 &amp; -2 &amp;-2 \\end{vmatrix}+1\\cdot\\begin{vmatrix}4 &amp; 0 &amp;2\\\\[1.1ex]3 &amp; 0 &amp; -1\\\\[1.1ex]1 &amp; -5 &amp; -2 \\end{vmatrix}-4\\cdot \\begin{vmatrix}4 &amp; 0 &amp; 2\\\\[1.1ex]3 &amp; 0 &amp; 4\\\\[1.1ex]1 &amp; -5 &amp; -2 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"553\" 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-39e083e5164c9719ef34fae3bcc2fe29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =3 \\cdot 50-2\\cdot(-50)+1\\cdot(-50)-4\\cdot 50\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"297\" 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-3de941669508660aa0a9173155a34685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =150+100-50-200\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"182\" style=\"vertical-align: -2px;\"><\/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-df99174f84ad1be8de3746d1ed3e245c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" 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-e8c9889f409b449fd7809f4e02394de2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6574\u4e2a\u6269\u5c55\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a\u96f6\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \u4e5f\u662f\u79e9\u4e3a 3 \u7684<\/strong>\u3002<\/p>\n<p>\u56e0\u6b64\u77e9\u9635 A \u548c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 3\uff0c\u56e0\u6b64<strong>\u4e24\u6761\u7ebf\u76f8\u4ea4<\/strong>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u4e4b\u95f4\u53ea\u6709\u4e00\u4e2a\u4ea4\u70b9\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48635c0a23e1d45677b03099c38205e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad rg(A) = rg(A')= 3 \\quad \\longrightarrow \\quad \\text{Rectas Secantes} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"488\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u4e0a\u9762\u6709\u4e00\u4e2a\u8868\u683c\uff0c\u5b83\u6839\u636e\u77e9\u9635 A \u548c A&#8217; \u7684\u8303\u56f4\u603b\u7ed3\u4e86\u4e24\u6761\u7ebf\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u6240\u6709\u53ef\u80fd\u60c5\u51b5\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-posicion-relativa-entre-dos-rectas-en-el-espacio\"><\/span>\u89e3\u51b3\u4e86\u7a7a\u95f4\u4e2d\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u627e\u5230\u4ee5\u4e0b\u4e24\u884c\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-0ee51f157ce008a022df46fc1930955e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ (x,y,z)=(3,4,0)+t(2,1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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-b3980ce534f631ae1f4781492158bcd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\ (x,y,z)=(1,-2,2)+t(0,5,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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\">\u7531\u4e8e\u4e24\u6761\u7ebf\u90fd\u8868\u793a\u4e3a\u77e2\u91cf\u65b9\u7a0b\uff0c\u56e0\u6b64\u6211\u4eec\u4f1a\u4ece\u6bcf\u6761\u7ebf\u7684\u4e00\u70b9\u4e00\u77e2\u91cf\u7684\u65b9\u6cd5\u6c42\u51fa\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002<\/p>\n<p class=\"has-text-align-left\">\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-0112cb63d5449bc1868594300ae69609_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(2,1,-3) \\qquad \\qquad \\vv{s}=(0,5,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"260\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5c5e\u4e8e\u6bcf\u6761\u7ebf\u7684\u70b9\u662f\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-62532678cedab3090235b715a54792d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R(3,4,0)\\qquad \\qquad S(1,-2,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8981\u5e94\u7528\u8be5\u8fc7\u7a0b\uff0c\u9996\u5148\u9700\u8981\u68c0\u67e5\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u662f\u5426\u6210\u6bd4\u4f8b\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-c9d7a07d74505c2794d50f3ecb878ed7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{0} \\neq \\cfrac{1}{5} \\neq \\cfrac{-3}{1} \\quad \\longrightarrow \\quad \\text{No proporcionales}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"314\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u4e24\u4e2a\u5411\u91cf\u4e0d\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u76f4\u7ebf\u53ea\u80fd\u76f8\u4ea4\u6216\u76f8\u4ea4\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u73b0\u5728\u9700\u8981\u6c42\u89e3\u4ee5\u4e0b\u7531\u65b9\u5411\u5411\u91cf\u548c\u6bcf\u6761\u7ebf\u4e0a\u7684\u70b9\u7ec4\u6210\u7684\u884c\u5217\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-225a68c152f54a250471b7c4c2254b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} \\text{v}}_x &amp; \\text{v}}_x' &amp; P_x-P_x' \\\\[1.1ex] \\text{v}}_y &amp; \\text{v}}_y' &amp; P_y-P_y' \\\\[1.1ex]\\text{v}}_z &amp; \\text{v}}_z' &amp; P_z-P_z' \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5b88268ae0a4248a6289d0f789250a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 2 &amp; 0 &amp; 3-1 \\\\[1.1ex] 1 &amp; 5 &amp; 4-(-2) \\\\[1.1ex]-3&amp; 1 &amp; 0-2 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u884c\u5217\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-99043262ed64a3fce660dc55e943a93a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 2 &amp; 0 &amp; 2 \\\\[1.1ex] 1 &amp; 5 &amp; 6 \\\\[1.1ex]-3&amp; 1 &amp; -2 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"125\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5224\u5b9a\u5668\u7684\u7ed3\u679c\u7b49\u4e8e 0\uff0c\u56e0\u6b64<strong>\u4e24\u6761\u7ebf\u76f8\u4ea4<\/strong>\u3002<\/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>\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u6761\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-1848a24fa2901265ca9b0d141c7e2d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  r: \\ \\begin{cases} x=3+2t \\\\[1.7ex] y=1+3t \\\\[1.7ex] z=2-t \\end{cases} \\qquad \\qquad s: \\ \\cfrac{x+1}{-4}=\\cfrac{y+5}{-6} = \\cfrac{z-4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"421\" 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\">\u7b2c\u4e00\u6761\u7ebf\u662f\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u7b2c\u4e8c\u6761\u7ebf\u662f\u8fde\u7eed\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u6bcf\u6761\u7ebf\u7684\u70b9\u5411\u91cf\u6cd5\u786e\u5b9a\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002<\/p>\n<p class=\"has-text-align-left\">\u53f3\u4fa7\u65b9\u5411\u5411\u91cf\u7684\u5750\u6807<\/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>\u662f\u53c2\u6570\u524d\u9762\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-3bdeeaff7b1444be22ec3b07e3219ac5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4ee5\u53ca\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u7684\u5750\u6807<\/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\u5206\u6bcd\u7684\u6570\u5b57\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-a5b857b3af4daf70ac0819c2c43dccce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(2,3,-1) \\qquad \\qquad \\vv{s}=(-4,-6,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5c5e\u4e8e\u6bcf\u6761\u7ebf\u7684\u70b9\u662f\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-5e174175d9f030d32e11a291f9478360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R(3,1,2)\\qquad \\qquad S(-1,-5,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8981\u5e94\u7528\u8be5\u8fc7\u7a0b\uff0c\u9996\u5148\u9700\u8981\u68c0\u67e5\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u662f\u5426\u6210\u6bd4\u4f8b\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-53e7c51a55384b233a7d54ad4a710600_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{-4} = \\cfrac{3}{-6}= \\cfrac{-1}{2} \\quad \\longrightarrow \\quad \\text{Proporcionales}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"316\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e24\u4e2a\u5411\u91cf\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u76f4\u7ebf\u53ea\u80fd\u5e73\u884c\u6216\u91cd\u5408\u3002\u4e3a\u4e86\u6d88\u9664\u8fd9\u4e2a\u7591\u95ee\uff0c\u9700\u8981\u5c06\u76f4\u7ebf\u4e0a\u7684\u70b9\u4ee3\u5165<\/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>\u5728\u76f4\u7ebf\u65b9\u7a0b\u4e2d<\/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>\uff08\u53cd\u4e4b\u4ea6\u7136\uff09\u770b\u770b\u5b83\u662f\u5426\u6ee1\u8db3\u6240\u8ff0\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-539533362856566b59b5d14d058dda23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R(3,1,2) \\ \\longrightarrow \\ \\cfrac{x+1}{-4}=\\cfrac{y+5}{-6} = \\cfrac{z-4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"294\" 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-ec6e9d0de4528399fec953e4db21063e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3+1}{-4}=\\cfrac{1+5}{-6} = \\cfrac{2-4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"170\" 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-4cfe9c6942d02fe58a00c5ee85055405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{-4}=\\cfrac{6}{-6} = \\cfrac{-2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"127\" 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-e236b00fec23266ff19f015885c2dbd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1=-1 = -1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"114\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u901a\u8fc7\u4ee3\u5165\u76f4\u7ebf\u4e0a\u7684\u70b9\uff0c\u6211\u4eec\u5f97\u5230\u4e00\u4e2a\u7b49\u5f0f\uff0c\u4f7f\u5f97\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u70b9\u6ee1\u8db3\u53e6\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u65b9\u7a0b\uff0c\u800c\u4e14\u5b83\u4eec\u7684\u65b9\u5411\u5411\u91cf\u6210\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c<strong>\u4e24\u6761\u7ebf\u91cd\u5408\u3002<\/strong><\/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>\u627e\u51fa\u4ee5\u4e0b\u4e24\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-33fbac4dc2933022ff39a0ed9d457200_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}2x-2y-2z+5=0 \\\\[2ex] 2x-y-1=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"206\" 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-8afae699c3b46dc2153236605e254fdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ \\begin{cases}4x-y+2z+3=0 \\\\[2ex] x-2y-3z+6=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"197\" 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\">\u4e24\u6761\u7ebf\u662f\u4e00\u822c\uff08\u6216\u9690\u542b\uff09\u65b9\u7a0b\u5f62\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u6392\u540d\u65b9\u6cd5\u6765\u67e5\u627e\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u5404\u884c\u7684\u7cfb\u6570\u5236\u4f5c\u77e9\u9635 A \u548c\u6269\u5c55\u77e9\u9635 A&#8217;\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-6133960b0b951ec6c455384a1b2274c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix}2 &amp; -2 &amp; -2\\\\[1.1ex]2 &amp; -1 &amp; 0\\\\[1.1ex]4 &amp; -1 &amp; 2\\\\[1.1ex]1 &amp; -2 &amp; -3\\end{pmatrix} \\qquad \\qquad A'=\\begin{pmatrix}2 &amp; -2 &amp; -2&amp;5\\\\[1.1ex]2 &amp; -1 &amp; 0&amp;-1\\\\[1.1ex]4 &amp; -1 &amp; 2&amp;3\\\\[1.1ex]1 &amp; -2 &amp; -3&amp;6  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"422\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u6709\u4e86\u4e24\u4e2a\u77e9\u9635\uff0c\u6211\u4eec\u5c31\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u6211\u4eec\u9996\u5148\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635 A \u7684\u79e9\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-18eb85dd3870c1e7c865705200cf6414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-85353e6e57de74332ffdb3d5cd44caaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}2 &amp; -2 &amp; -2\\\\[1.1ex]2 &amp; -1 &amp; 0\\\\[1.1ex]4 &amp; -1 &amp; 2 \\end{vmatrix} =0 \\qquad \\begin{vmatrix}2 &amp; -2 &amp; -2\\\\[1.1ex]2 &amp; -1 &amp; 0\\\\[1.1ex]1 &amp; -2 &amp; -3 \\end{vmatrix}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"298\" 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-d33b143e636093057c08fbcd9d91ab54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}2 &amp; -2 &amp; -2\\\\[1.1ex]4 &amp; -1 &amp; 2\\\\[1.1ex]1 &amp; -2 &amp; -3 \\end{vmatrix} =0 \\qquad \\begin{vmatrix}2 &amp; -1 &amp; 0\\\\[1.1ex]4 &amp; -1 &amp; 2\\\\[1.1ex]1 &amp; -2 &amp; -3 \\end{vmatrix}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"298\" 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-5b4b570b6d9d92b7974b11afbe0939bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}2 &amp; -2 \\\\[1.1ex]2 &amp; -1 \\end{vmatrix}=2 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"123\" 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-6865ac4ae80c8b5a6eff791a9da5a937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u77e9\u9635 A \u7684\u6240\u6709 3&#215;3 \u884c\u5217\u5f0f\u5747\u4e3a\u96f6\uff0c\u4f46\u77e9\u9635\u5185\u90e8\u6709\u4e00\u4e2a\u975e\u96f6 2&#215;2 \u884c\u5217\u5f0f\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 2<\/strong> \u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u6269\u5c55\u77e9\u9635A&#8217;\u7684\u8303\u56f4\u3002\u77e9\u9635 A&#8217; \u603b\u662f\u81f3\u5c11\u662f\u77e9\u9635 A \u7684\u8303\u56f4\uff0c\u5728\u672c\u4f8b\u4e2d\u4e3a 2\uff0c\u56e0\u6b64\u6709\u5fc5\u8981\u68c0\u67e5\u5b83\u662f\u5426\u6709\u4e00\u4e2a\u4e0d\u53d6\u6d88\u7684 3\u00d73 \u884c\u5217\u5f0f\uff0c\u4ee5\u53ca\u8be5\u884c\u5217\u5f0f\u7684\u884c\u5217\u5f0f\u662f\u591a\u5c11\u3002\u6574\u4e2a\u77e9\u9635\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-d97c98cb8c416b0ce39b18628124923c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-d253c404b2ac9caf3119795e80acfbfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\displaystyle \\begin{vmatrix}2 &amp; -2 &amp; 5\\\\[1.1ex]2 &amp; -1 &amp;-1\\\\[1.1ex]4 &amp; -1 &amp;3\\end{vmatrix}=22 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"170\" 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-8744aa6a413d43832344c6eba827c7e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle det(A')=\\begin{vmatrix}2 &amp; -2 &amp; -2&amp;5\\\\[1.1ex]2 &amp; -1 &amp; 0&amp;-1\\\\[1.1ex]4 &amp; -1 &amp; 2&amp;3\\\\[1.1ex]1 &amp; -2 &amp; -3&amp;6 \\end{vmatrix}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"249\" 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-e8c9889f409b449fd7809f4e02394de2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6269\u5c55\u77e9\u9635 A&#8217; \u786e\u5b9e\u5305\u542b 3\u00d73 \u4e2a\u975e\u96f6\u5b50\u884c\u5217\u5f0f\uff0c\u800c\u4e14\u6574\u4e2a\u6269\u5c55\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7b49\u4e8e 0\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 3<\/strong> \u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 2\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 3\uff0c\u56e0\u6b64<strong>\u4e24\u6761\u7ebf\u662f\u5e73\u884c\u7684<\/strong>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u6ca1\u6709\u4efb\u4f55\u5171\u540c\u70b9\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-042e97ffdc2f223e6a3ba51d9f942b5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad rg(A) = 2 \\neq rg(A')= 3 \\quad \\longrightarrow \\quad \\text{Rectas Paralelas} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"525\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u8bb0\u4f4f\uff0c\u5728\u65b9\u6cd5\u7684\u8bf4\u660e\uff08\u4e0a\u9762\uff09\u4e2d\uff0c\u60a8\u6709\u4e00\u4e2a\u8868\u683c\uff0c\u6839\u636e\u77e9\u9635 A \u548c A&#8217; \u7684\u7b49\u7ea7\u603b\u7ed3\u4e86\u4e24\u6761\u7ebf\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u6240\u6709\u53ef\u80fd\u60c5\u51b5\u3002<\/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>\u627e\u51fa\u4ee5\u4e0b\u4e24\u884c\u7684\u76f8\u5bf9\u4f4d\u7f6e\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-b39d8ac101e2b4db7f5a17a3f27066b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}4x-y+2z=0 \\\\[2ex] x+y+3z-1=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" 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-ddbbfa691034e2f7acd17d6391e9719e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ \\begin{cases}2x+5y-z-2=0 \\\\[2ex] 2x+3z+1=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"197\" 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\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u6761\u7ebf\u662f\u7b1b\u5361\u5c14\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u5f62\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u6392\u5e8f\u65b9\u6cd5\u6765\u67e5\u627e\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u5404\u884c\u7684\u7cfb\u6570\u6784\u9020\u77e9\u9635 A \u548c\u6269\u5c55\u77e9\u9635 A&#8217;\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-cfc6a66630bf6a5cc24f5a006db629af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix}4 &amp; -1 &amp; 2\\\\[1.1ex]1 &amp; 1 &amp; 3\\\\[1.1ex]2 &amp; 5 &amp; -1\\\\[1.1ex]2 &amp; 0 &amp; 3 \\end{pmatrix} \\qquad \\qquad A'=\\begin{pmatrix}4 &amp; -1 &amp; 2&amp;0\\\\[1.1ex]1 &amp; 1 &amp; 3&amp;-1\\\\[1.1ex]2 &amp; 5 &amp; -1&amp;-2\\\\[1.1ex]2 &amp; 0 &amp; 3 &amp;1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"422\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u4e24\u4e2a\u77e9\u9635\uff0c\u6211\u4eec\u5c31\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u6211\u4eec\u9996\u5148\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635 A \u7684\u79e9\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-18eb85dd3870c1e7c865705200cf6414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-7a682d947fc58cb847cb2dd60f8772d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}4 &amp; -1 &amp; 2\\\\[1.1ex]1 &amp; 1 &amp; 3\\\\[1.1ex]2 &amp; 5 &amp; -1 \\end{vmatrix}  = -65 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"179\" 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-466d66279a42e8aeb422d568e1547ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u77e9\u9635 A \u5305\u542b\u4e00\u4e2a 3\u00d73 \u5b50\u77e9\u9635\uff0c\u5176\u884c\u5217\u5f0f\u975e\u96f6\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 3<\/strong> \u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u6269\u5c55\u77e9\u9635A&#8217;\u7684\u8303\u56f4\u3002\u77e9\u9635 A&#8217; \u59cb\u7ec8\u81f3\u5c11\u5177\u6709\u77e9\u9635 A \u7684\u79e9\uff0c\u5728\u672c\u4f8b\u4e2d\u5176\u503c\u4e3a 3\uff0c\u56e0\u6b64\u68c0\u67e5\u5b83\u7684\u79e9\u662f 4 \u8fd8\u662f 3 \u5c31\u8db3\u591f\u4e86\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u6c42\u89e3\u4ee5\u4e0b\u884c\u5217\u5f0f\u7531\u52a0\u6cd5\uff08\u6216\u8f85\u56e0\u5b50\uff09\u7ec4\u6210\u7684 4\u00d74 \u77e9\u9635\u7684\u96c6\u5408\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-d97c98cb8c416b0ce39b18628124923c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-fc223e99519a7cc9359cb6e08591e039_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle det(A')=\\begin{vmatrix}4 &amp; -1 &amp; 2&amp;0\\\\[1.1ex]1 &amp; 1 &amp; 3&amp;-1\\\\[1.1ex]2 &amp; 5 &amp; -1&amp;-2\\\\[1.1ex]2 &amp; 0 &amp; 3 &amp;1 \\end{vmatrix} =\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"234\" 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-ed6f0611953cbd025d6e3bed38994fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =4 \\cdot\\begin{vmatrix} 1 &amp; 3&amp;-1\\\\[1.1ex] 5 &amp; -1&amp;-2\\\\[1.1ex] 0 &amp; 3 &amp;1 \\end{vmatrix}-(-1)\\cdot\\begin{vmatrix}1  &amp; 3&amp;-1\\\\[1.1ex]2 &amp; -1 &amp; -2\\\\[1.1ex]2 &amp; 3 &amp;1 \\end{vmatrix}+2\\cdot\\begin{vmatrix}1 &amp; 1 &amp;-1\\\\[1.1ex]2 &amp; 5 &amp; -2\\\\[1.1ex]2 &amp; 0 &amp;1 \\end{vmatrix}-0\\cdot \\begin{vmatrix}1 &amp; 1 &amp; 3\\\\[1.1ex]2 &amp; 5 &amp; -1\\\\[1.1ex]2 &amp; 0 &amp; 3 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"553\" 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-a7873f68c97807b541c64943ddddfa4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =4 \\cdot(-25)+1\\cdot(-21)+2\\cdot 9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"227\" 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-b1575ce994cf8d65216e53d682fa4403_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =-100-21+18\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"138\" style=\"vertical-align: -2px;\"><\/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-6184cc67c626c38b308144a4114a4de4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle =-103\\bm{\\neq0}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" 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-bd9638d9df3f5ccb112e984363d10da6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A')=4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6574\u4e2a\u6269\u5c55\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 4<\/strong> \u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 3\uff0c\u76f8\u53cd\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 4\uff0c\u56e0\u6b64<strong>\u4e24\u6761\u7ebf\u76f8\u4ea4<\/strong>\u4e8e\u4e00\u70b9\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-449445957cebd657da5bda15f232ee56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black} \\quad rg(A) = 3 \\neq rg(A')= 4 \\quad \\longrightarrow \\quad \\text{Rectas se cruzan} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"527\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u8bb0\u4f4f\uff0c\u5728\u4e0a\u9762\u7684\u8fc7\u7a0b\u8bf4\u660e\u4e2d\uff0c\u60a8\u6709\u4e00\u4e2a\u8868\u683c\uff0c\u5176\u4e2d\u6839\u636e\u77e9\u9635 A \u548c A&#8217; \u7684\u7b49\u7ea7\uff0c\u5217\u51fa\u4e86\u4e24\u6761\u7ebf\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u6240\u6709\u53ef\u80fd\u60c5\u51b5\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u7a7a\u95f4\u4e2d\u4e24\u6761\u7ebf\u7684\u6240\u6709\u76f8\u5bf9\u4f4d\u7f6e\uff08\u5728 R3 \u4e2d\uff09\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u89e3\u91ca\u4e86\u5982\u4f55\u4f7f\u7528\u4e24\u79cd\u53ef\u80fd\u7684\u65b9\u6cd5\u627e\u5230\u4e24\u6761\u7ebf\u4e4b\u95f4 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e6%9d%a1%e7%ba%bf%e7%9a%84%e7%9b%b8%e5%af%b9%e4%bd%8d%e7%bd%ae-r3-%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u4e24\u6761\u7ebf\u5728\u7a7a\u95f4\u4e2d\u7684\u76f8\u5bf9\u4f4d\u7f6e<\/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-247","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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