{"id":248,"date":"2023-07-10T12:11:22","date_gmt":"2023-07-10T12:11:22","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e4%b8%aa%e5%b9%b3%e9%9d%a2%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":"2023-07-10T12:11:22","modified_gmt":"2023-07-10T12:11:22","slug":"%e7%a9%ba%e9%97%b4%e4%b8%ad%e4%b8%a4%e4%b8%aa%e5%b9%b3%e9%9d%a2%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%e4%b8%aa%e5%b9%b3%e9%9d%a2%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\u4e2a\u5e73\u9762\u5728\u7a7a\u95f4\u4e2d\u7684\u76f8\u5bf9\u4f4d\u7f6e"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u4e24\u4e2a\u5e73\u9762\uff08\u5e72\u71e5\u5e73\u9762\u3001\u5e73\u884c\u5e73\u9762\u6216\u91cd\u5408\u5e73\u9762\uff09\u7684\u6240\u6709\u53ef\u80fd\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u67e5\u770b\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-las-posiciones-relativas-de-dos-planos\"><\/span>\u4e24\u4e2a\u5e73\u9762\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\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u53ea\u6709\u4e09\u79cd\u53ef\u80fd\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff1a\u5272\u5e73\u9762\u3001\u5e73\u884c\u5e73\u9762\u548c\u91cd\u5408\u5e73\u9762\u3002<\/p>\n<ul>\n<li><strong>\u76f8\u4ea4\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u4ec5\u76f8\u4ea4\u4e8e\u4e00\u6761\u76f4\u7ebf\uff0c\u5219\u4e24\u4e2a\u5e73\u9762\u76f8\u4ea4\u3002<\/li>\n<li><strong>\u5e73\u884c\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u5728\u4efb\u4f55\u4e00\u70b9\u90fd\u4e0d\u76f8\u4ea4\uff0c\u5219\u5b83\u4eec\u5e73\u884c\u3002<\/li>\n<li><strong>\u91cd\u5408\u5e73\u9762<\/strong>\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u9762\u90fd\u6709\u516c\u5171\u70b9\uff0c\u5219\u4e24\u4e2a\u5e73\u9762\u91cd\u5408\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-72\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u76f8\u4ea4\u5e73\u9762<\/strong><\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-secants.webp\" alt=\"\u4e24\u4e2a\u76f8\u4ea4\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2814\" width=\"265\" height=\"258\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u5e73\u884c\u5e73\u9762<\/strong><\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-paralleles-1.webp\" alt=\"\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2815\" width=\"266\" height=\"166\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"><strong>\u91cd\u5408\u5e73\u9762<\/strong><\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/deux-avions-coincidents.webp\" alt=\"\u4e24\u4e2a\u91cd\u5408\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2820\" width=\"294\" height=\"83\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u6c42\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u6709\u4e24\u79cd\u65b9\u6cd5\uff1a\u4e00\u79cd\u662f\u6839\u636e\u4e24\u4e2a\u5e73\u9762\u7684\u4e00\u822c\u65b9\u7a0b\u7684\u7cfb\u6570\uff0c\u53e6\u4e00\u79cd\u662f\u901a\u8fc7\u8ba1\u7b97\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u4e0b\u9762\u662f\u6bcf\u4e2a\u8fc7\u7a0b\u7684\u89e3\u91ca\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-determinar-la-posicion-relativa-de-dos-planos-por-coeficientes\"><\/span>\u5982\u4f55\u901a\u8fc7\u7cfb\u6570\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u76f8\u5bf9\u4f4d\u7f6e\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u5b83\u4eec\u7684\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u7684\u7cfb\u6570\u3002<\/p>\n<p>\u7136\u540e\u8003\u8651\u4e24\u4e2a\u4e0d\u540c\u5e73\u9762\u7684\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a363201f1d61e53c35c3484a0fe116d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"221\" 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-330dffa3582cfbd92e893f755d2b06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A'x+B'y+C'z+D'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"240\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff08\u5728 R3 \u4e2d\uff09\u53d6\u51b3\u4e8e\u5b83\u4eec\u7684\u7cfb\u6570\u6216\u53c2\u6570\u7684\u6bd4\u4f8b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/position-relative-de-deux-plans-avec-parametres.webp\" alt=\"\u5e26\u53c2\u6570\u7684\u4e24\u4e2a\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\" class=\"wp-image-2825\" width=\"483\" height=\"263\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u5f53\u7cfb\u6570 A\u3001B \u6216 C \u4e4b\u4e00\u4e0e\u5176\u4ed6\u7cfb\u6570\u4e0d\u6210\u6bd4\u4f8b\u65f6\uff0c\u4e24\u4e2a\u5e73\u9762\u5c06\u76f8\u4ea4\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u53ea\u6709\u72ec\u7acb\u9879\u4e0d\u6210\u6bd4\u4f8b\u65f6\uff0c\u4e24\u4e2a\u5e73\u9762\u5c06\u5e73\u884c\u3002\u6700\u540e\uff0c\u5f53\u4e24\u4e2a\u65b9\u7a0b\u7684\u6240\u6709\u7cfb\u6570\u6210\u6bd4\u4f8b\u65f6\uff0c\u8ba1\u5212\u5c06\u91cd\u5408\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\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-06ccd4d459bd8e4a4bfaa7722389c8ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x-2y+4z+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" 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-0dc2e5222b977e7e3a1a3070b26ef4a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -3x+y-2z+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"205\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u8981\u77e5\u9053\u5b83\u662f\u4ec0\u4e48\u7c7b\u578b\u7684\u98de\u673a\uff0c\u60a8\u9700\u8981\u68c0\u67e5\u54ea\u4e9b\u7cfb\u6570\u662f\u6210\u6bd4\u4f8b\u7684\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdce7ece2e3d326c1768ec8435fbb12c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{-3} = \\cfrac{-2}{1} =\\cfrac{4}{-2} \\neq \\cfrac{5}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"162\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7cfb\u6570A\u3001B\u3001C\u5f7c\u6b64\u6210\u6b63\u6bd4\uff0c\u4f46\u4e0e\u7cfb\u6570D\u4e0d\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64<strong>\u4e24\u4e2a\u5e73\u9762\u5e73\u884c<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-posicion-relativa-de-dos-planos-por-rangos\"><\/span>\u5982\u4f55\u901a\u8fc7\u8303\u56f4\u8ba1\u7b97\u4e24\u4e2a\u5e73\u9762\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>\u83b7\u77e5\u4e24\u4e2a\u786e\u5b9a\u7684\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\u7684\u53e6\u4e00\u79cd\u65b9\u5f0f\u5305\u62ec\u8ba1\u7b97\u7531\u6240\u8ff0\u5e73\u9762\u7684\u7cfb\u6570\u5f62\u6210\u7684\u4e24\u4e2a\u77e9\u9635\u7684\u8303\u56f4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u6210\u4e3a\u4e24\u4e2a\u4e0d\u540c\u5e73\u9762\u7684\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a363201f1d61e53c35c3484a0fe116d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"221\" 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-330dffa3582cfbd92e893f755d2b06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A'x+B'y+C'z+D'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"240\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u4e24\u4e2a\u65b9\u7a0b\u7684\u7cfb\u6570 A\u3001B \u548c C \u7ec4\u6210\u7684\u77e9\u9635\u79f0\u4e3a A\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-37f97413606a79781a34e0664a780b35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} A&amp;B&amp;C\\\\[1.1ex] A&amp;B&amp;C\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4ee4\u77e9\u9635 A&#8217; \u4e3a\u5305\u542b\u4e24\u4e2a\u65b9\u7a0b\u6240\u6709\u7cfb\u6570\u7684\u5c55\u5f00\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-534e5baa11d1331cda0fa48c167a322f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A' =\\begin{pmatrix} A&amp;B&amp;C&amp;D\\\\[1.1ex] A&amp;B&amp;C&amp;D'\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6839\u636e\u524d\u9762\u4e24\u4e2a\u77e9\u9635\u7684\u8303\u56f4\u53ef\u4ee5\u77e5\u9053\u4e24\u4e2a\u5e73\u9762\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff1a<\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><\/figure>\n<p> Rouche-Frobenius toerem\uff08\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u5b9a\u7406\uff09\u53ef\u4ee5\u8bc1\u660e\u76f8\u5bf9\u4f4d\u7f6e\u53d6\u51b3\u4e8e\u8fd9\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u4e0d\u8fc7\uff0c\u5728\u672c\u9875\u4e2d\u6211\u4eec\u4e0d\u4f1a\u8fdb\u884c\u6f14\u793a\uff0c\u56e0\u4e3a\u6ca1\u6709\u5fc5\u8981\u4e86\u89e3\u5b83\uff0c\u800c\u4e14\u5b83\u4e5f\u6ca1\u6709\u63d0\u4f9b\u592a\u591a\u5185\u5bb9\u3002<\/p>\n<p>\u6240\u4ee5\u4f60\u53ef\u4ee5\u770b\u5230\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\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-bb7ab1c6ff6922119d6c9bdf8d00185d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 2x+3y-z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" 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-615620cd79e191209135368785788ed5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x-4y+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\u8981\u505a\u7684\u662f\u7528\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\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-c5cfb4d05d76542970c1f7db9ef1b31a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} 2&amp;3&amp;-1\\\\[1.1ex] 3&amp;-4&amp;0\\end{pmatrix} \\qquad \\qquad A' =\\begin{pmatrix} 2&amp;3&amp;-1&amp;1\\\\[1.1ex] 3&amp;-4&amp;0&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"402\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u77e9\u9635\u7684\u79e9\u3002\u6211\u4eec\u9996\u5148\u901a\u8fc7\u884c\u5217\u5f0f\u6c42\u51fa\u77e9\u9635 A \u7684\u8303\u56f4\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-5db59e1c8bbf94b95483870d47cea1b2_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-2ad5c0df1a15c695be7c0c5c71304cc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2&amp;3\\\\[1.1ex] 3&amp;-4\\end{vmatrix} =-17\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" 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-ef18656c1a261aa20598fc8f6a587323_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>\u77e9\u9635 A \u5305\u542b\u4e00\u4e2a 2\u00d72 \u5b50\u77e9\u9635\uff0c\u5176\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff0c\u56e0\u6b64\u5b83\u662f\u4e00\u4e2a\u79e9\u4e3a 2 \u7684\u77e9\u9635\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8fd8\u9700\u8981\u8ba1\u7b97\u77e9\u9635A&#8217;\u7684\u79e9\u3002\u5e76\u4e14\u6269\u5c55\u77e9\u9635 A&#8217; \u7684\u79e9\u5c06\u59cb\u7ec8\u81f3\u5c11\u4e0e\u77e9\u9635 A \u7684\u79e9\u76f8\u540c\uff0c\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u7b49\u4e8e 2\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-c233de165178bb10a2af16fcdcba7412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A') = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f7f\u5f97\u4e24\u4e2a\u77e9\u9635\u7684\u8303\u56f4\u76f8\u7b49\u5e76\u4e14\u503c\u4e3a2\uff0c\u56e0\u6b64<strong>\u4e24\u4e2a\u5e73\u9762\u76f8\u4ea4<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-posicion-relativa-de-dos-planos\"><\/span>\u89e3\u51b3\u4e86\u4e24\u4e2a\u5e73\u9762\u76f8\u5bf9\u4f4d\u7f6e\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u7814\u7a76\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\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-98683696adfea865d08a178dd9ba0254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+3y-2z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" 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-2f74673e269babed8b8307b75abe8864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+9y-6z-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/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\u8ba1\u7b97\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u6211\u4eec\u8981\u770b\u770b\u4e24\u4e2a\u5e73\u9762\u7684\u65b9\u7a0b\u7684\u7cfb\u6570\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-c3fdba96e5ae97a2461c53ba81ce0f6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{3}= \\cfrac{3}{9} =\\cfrac{-2}{-6} = \\cfrac{-1}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"156\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e24\u4e2a\u5e73\u9762\u7684\u9690\u5f0f\u65b9\u7a0b\u7684\u6240\u6709\u7cfb\u6570\u90fd\u6210\u6b63\u6bd4\uff0c<strong>\u56e0\u6b64\u662f\u4e24\u4e2a\u91cd\u5408\u5e73\u9762<\/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>\u786e\u5b9a\u4e0b\u5217\u4e24\u4e2a\u5e73\u9762\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-bb9ae2ea33c20a52892a0a0a1916d1a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+3y-z+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"182\" 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-ed4d3289afe5e58aa256afcb9937ae0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 2x+3y-2z+8=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/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\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u6211\u4eec\u6765\u5206\u6790\u5b83\u4eec\u65b9\u7a0b\u7684\u7cfb\u6570\u7684\u6bd4\u4f8b\u5173\u7cfb\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-9c1a39300d950ead0a79224572064ee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} \\neq \\cfrac{3}{3} \\neq \\cfrac{-1}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e24\u4e2a\u5e73\u9762\u7684\u9690\u5f0f\u65b9\u7a0b\u7684\u7cfb\u6570A\u548cC\u5f7c\u6b64\u6210\u6b63\u6bd4\uff0c\u4f46\u4e0e\u7cfb\u6570B\u4e0d\u6210\u6bd4\u4f8b<strong>\u3002\u56e0\u6b64\u5b83\u4eec\u662f\u4e24\u4e2a\u5272\u5e73\u9762<\/strong>\u3002<\/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>\u6c42\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\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-acb264b7b74aa4dc951d87efb7708a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x-3y-12z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"209\" 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-30503eab848d5849c33533bbd31a8f0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -2x+y+4z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"205\" style=\"vertical-align: -4px;\"><\/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\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u9700\u8981\u68c0\u67e5\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\u7684\u7cfb\u6570\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-8e3df6a5267721b19719d5cf5fdd6681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{-2} = \\cfrac{-3}{1} =\\cfrac{-12}{4} \\neq \\cfrac{7}{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"192\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e24\u4e2a\u5e73\u9762\u65b9\u7a0b\u7684\u524d\u4e09\u4e2a\u53c2\u6570\uff08A\u3001B\u3001C\uff09\u5f7c\u6b64\u6210\u6b63\u6bd4\uff0c\u4f46\u4e0e\u53c2\u6570D\u4e0d\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64<strong>\u4e24\u4e2a\u5e73\u9762\u5e73\u884c<\/strong>\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>\u8ba1\u7b97\u53c2\u6570\u503c<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f7f\u5f97\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\u5e73\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-3f76595910ed6f4bda73af19268183f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x-3y+5z+3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" 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-cafaa5f6f87852bbfc799e1de7df7438_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 2x-6y+az-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"201\" style=\"vertical-align: -4px;\"><\/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\u4f7f\u4e24\u4e2a\u5e73\u9762\u5e73\u884c\uff0c\u5b83\u4eec\u65b9\u7a0b\u4e2d\u7684\u7cfb\u6570 A\u3001B \u548c C \u5fc5\u987b\u6210\u6bd4\u4f8b\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5fc5\u987b\u9a8c\u8bc1\u4ee5\u4e0b\u7b49\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-ce428f1ffcead4e478675ac0c7af7fd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{-3}{-6} = \\cfrac{5}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\uff0c\u7b2c\u4e00\u4e2a\u8ba1\u5212\u7684\u7cfb\u6570 A \u548c B \u662f\u7b2c\u4e8c\u4e2a\u8ba1\u5212\u7684\u4e00\u534a\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-fd9f9f85f6ba71dc375ebf245b156714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{5}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u6c42\u89e3\u4e0a\u9762\u7684\u65b9\u7a0b\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4e24\u4e2a\u5206\u6570\u76f8\u4ea4\u53c9\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-9054a7621d7ca298b229a7aa522ca31b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot a=5 \\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"83\" 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-dda10217783919119a8704d3f875327e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=10}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u53c2\u6570\u7684\u503c<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5fc5\u987b\u7b49\u4e8e 10\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end 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