{"id":258,"date":"2023-07-10T07:15:20","date_gmt":"2023-07-10T07:15:20","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e5%90%91%e9%87%8f\/"},"modified":"2023-07-10T07:15:20","modified_gmt":"2023-07-10T07:15:20","slug":"%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e5%90%91%e9%87%8f\/","title":{"rendered":"\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u5411\u91cf"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u5171\u9762\u5411\u91cf\u4ee5\u53ca\u5982\u4f55\u5224\u65ad 2\u30013\u30014 \u6216\u66f4\u591a\u5411\u91cf\u662f\u5426\u5171\u9762\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u5171\u9762\u5411\u91cf\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-vectores-coplanarios\"><\/span>\u4ec0\u4e48\u662f\u5171\u9762\u5411\u91cf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u5411\u91cf\u7684\u542b\u4e49\u5982\u4e0b\uff1a<\/p>\n<p><strong>\u5171\u9762\u5411\u91cf\u662f\u5c5e\u4e8e\u540c\u4e00\u5e73\u9762\u7684\u5411\u91cf\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u5411\u91cf\u603b\u662f\u5171\u9762\u7684\uff0c\u56e0\u4e3a\u4e00\u4e2a\u5e73\u9762\u53ea\u9700 2 \u4e2a\u5411\u91cf\u5373\u53ef\u5f62\u6210\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u5b58\u57283\u4e2a\u30014\u4e2a\u6216\u66f4\u591a\u4e2a\u77e2\u91cf\u65f6\uff0c\u5176\u4e2d\u4e00\u4e2a\u77e2\u91cf\u53ef\u80fd\u4e0d\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\uff0c\u56e0\u6b64\u5b83\u4eec\u4e0d\u5171\u9762\u3002 <\/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\/vecteurs-coplanaires-ou-coplanaires.webp\" alt=\"\u5171\u9762\u6216\u5171\u9762\u5411\u91cf\u7684\u793a\u4f8b\" class=\"wp-image-3133\" width=\"353\" height=\"171\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4f8b\u5982\uff0c\u5728\u4e0a\u56fe\u4e2d\u60a8\u53ef\u4ee5\u770b\u5230\u5411\u91cf<\/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-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4eec\u5f7c\u6b64\u5171\u9762\uff0c\u56e0\u4e3a\u5b83\u4eec\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u8fd9\u4e24\u4e2a\u5411\u91cf\u4e0e\u5411\u91cf\u4e0d\u5171\u9762<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4bbbc56786695092eac40831aee80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u56e0\u4e3a\u5728\u5305\u542b\u4e09\u4e2a\u5411\u91cf\u7684\u7a7a\u95f4\u4e2d\u65e0\u6cd5\u5f62\u6210\u5e73\u9762\u3002<\/p>\n<p>\u4ece\u8fd9\u4e2a\u5c5e\u6027\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad\uff0c\u5982\u679c 3 \u4e2a\u6216\u66f4\u591a\u5411\u91cf\u5171\u9762\uff0c\u5219\u5b9a\u4e49\u6240\u8ff0\u5411\u91cf\u7684\u70b9\uff08\u5411\u91cf\u7684\u8d77\u70b9\u548c\u7ec8\u70b9\uff09\u4e5f\u662f\u5171\u9762\u70b9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuando-los-vectores-son-coplanarios\"><\/span>\u5411\u91cf\u4ec0\u4e48\u65f6\u5019\u5171\u9762\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u5411\u91cf\u7684\u5b9a\u4e49\u4e2d\u770b\u5230\u7684\uff0c\u4e24\u4e2a\u5411\u91cf\u59cb\u7ec8\u5171\u9762\uff0c\u4f46\u4e24\u4e2a\u4ee5\u4e0a\u7684\u5411\u91cf\u4e0d\u5fc5\u9075\u5b88\u5171\u9762\u5173\u7cfb\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6709\u51e0\u79cd\u65b9\u6cd5\u53ef\u4ee5\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u5411\u91cf\u662f\u5426\u5171\u9762\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u4e09\u4e2a\u5411\u91cf\u7684\u6df7\u5408\u79ef\uff08\u6216\u4e09\u91cd\u70b9\u79ef\uff09\u7b49\u4e8e\u96f6\uff0c\u5219\u8868\u793a\u4e09\u4e2a\u5411\u91cf\u5171\u9762\u3002\u5982\u679c\u60a8\u4e0d\u592a\u6e05\u695a\u8fd9\u4e2a\u8fd0\u7b97\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff0c\u6211\u5efa\u8bae\u60a8\u770b\u4e00\u4e0b<a href=\"https:\/\/mathority.org\/cn\/\u4e09\u4e2a\u5411\u91cf\u6216\u4e09\u91cd\u6807\u91cf\u79ef\u7684\u6df7\u5408\u79ef\u793a\u4f8b\/\">\u4ec0\u4e48\u662f\u4e09\u4e2a\u5411\u91cf\u7684\u6df7\u5408\u79ef<\/a>\uff0c\u5728\u8fd9\u91cc\u60a8\u53ef\u4ee5\u627e\u5230\u89e3\u91ca\u4ee5\u53ca\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/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-849b07c1e268c4903e7bd13ef56bcaf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] =0\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"92\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u4e00\u7ec4\u5411\u91cf\u53ef\u4ee5\u8868\u793a\u4e3a<a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u4e24\u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c<\/a>\u5219\u610f\u5473\u7740\u5b83\u4eec\u662f\u5171\u9762\u7684\uff0c\u8fd9\u610f\u5473\u7740 3 \u4e2a\u6216\u66f4\u591a\u5411\u91cf\u5f53\u4e14\u4ec5\u5f53\u5b83\u4eec\u7ebf\u6027\u76f8\u5173\u65f6\u624d\u662f\u5171\u9762\u7684\u3002\u4e3a\u4e86\u8868\u660e\u4e09\u4e2a\u6216\u66f4\u591a\u5411\u91cf\u662f\u4e24\u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u6240\u6709\u5411\u91cf\u5f62\u6210\u7684\u77e9\u9635\u7684\u79e9\u7b49\u4e8e2\u5c31\u8db3\u591f\u4e86\u3002<\/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-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>\u91cd\u8981\u7684\u662f\uff0c\u60a8\u5fc5\u987b\u5145\u5206\u7406\u89e3<a href=\"https:\/\/mathority.org\/cn\/\u72ec\u7acb\u548c\u7ebf\u6027\u76f8\u5173\u5411\u91cf-\u72ec\u7acb-\u7ebf\u6027\u76f8\u5173\/\">\u7ebf\u6027\u76f8\u5173\u6027\u548c\u72ec\u7acb\u6027<\/a>\u7684\u6982\u5ff5\uff0c\u5373\u4e24\u4e2a\u5411\u91cf\u4f55\u65f6\u7ebf\u6027\u76f8\u5173\u6216\u7ebf\u6027\u72ec\u7acb\u4ee5\u53ca\u8fd9\u610f\u5473\u7740\u4ec0\u4e48\u3002\u5982\u679c\u60a8\u4e0d\u5b8c\u5168\u6e05\u695a\uff0c\u5728\u94fe\u63a5\u4e2d\u60a8\u4f1a\u627e\u5230\u975e\u5e38\u8be6\u7ec6\u7684\u89e3\u91ca\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002<\/p>\n<ul>\n<li>\u5982\u679c\u6240\u8ba8\u8bba\u7684\u5411\u91cf\u662f<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u884c\u5411\u91cf\/\">\u5e73\u884c\u5411\u91cf<\/a>\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u4e5f\u662f\u5171\u9762\u7684\uff0c\u5373\u6240\u6709\u5e73\u884c\u5411\u91cf\u90fd\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\u3002 <\/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-4efa93d26f00c6abc1180201f84d126a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\parallel  \\vv{\\text{v}} \\parallel \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-vectores-coplanarios\"><\/span>\u89e3\u51b3\u4e86\u5171\u9762\u5411\u91cf\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u5224\u65ad\u4ee5\u4e0b\u4e09\u4e2a\u5411\u91cf\u662f\u5426\u5171\u9762\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-16f2fe8ce9dccfd2f5f2b26461ca54e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-ce008f944cfd9efa2c48d0083a479c89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (2,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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-d8759d1ec233d68fc5f81dfb3b67beb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (-1,-5,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u68c0\u67e5\u8fd9\u662f\u5426\u662f 3 \u4e2a\u5171\u9762\u5411\u91cf\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u8fd9\u4e09\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u6df7\u5408\u79ef\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-2a1e4b0655c0a3f0165c880f5e64cce0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 3 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 3 &amp; -1 \\\\[1.1ex] -1 &amp; -5 &amp; 4 \\end{vmatrix} \\\\[2ex] &amp;= 36+1-20+6-15-8 \\\\[2ex] &amp; = \\bm{0} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"271\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e09\u4e2a\u5411\u91cf\u7684\u6df7\u5408\u79ef\u4e3a\u96f6\uff0c\u56e0\u6b64<strong>\u4e09\u4e2a\u5411\u91cf\u5171\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>\u5224\u65ad\u4ee5\u4e0b\u4e09\u4e2a\u5411\u91cf\u662f\u5426\u5171\u9762\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-a7c6550cedc0ccb79a9bfdebdd9987cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (4,-2,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-730594e946d69d5c0bd66b4b6d0f443c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" 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-a85ef59d300497c53b26259f19df79f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (6,-3,9)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" 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\">\u68c0\u67e5\u6211\u4eec\u662f\u5426\u6b63\u5728\u5904\u7406 3 \u4e2a\u5171\u9762\u5411\u91cf\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u6c42\u89e3\u4e09\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u6df7\u5408\u79ef\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u4ed4\u7ec6\u89c2\u5bdf\u5411\u91cf\u7684\u5206\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5b83\u4eec\u662f\u6210\u6bd4\u4f8b\u7684\u3002\u56e0\u6b64\uff0c\u8fd9\u4e09\u4e2a\u5411\u91cf\u5f7c\u6b64\u5e73\u884c\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-0c5ac41bb15ea29bdc9736f100d1cf74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\parallel \\vv{\\text{v}} \\parallel \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u6240\u6709\u5411\u91cf\u90fd\u662f\u5e73\u884c\u7684\uff0c<strong>\u56e0\u6b64\u5b83\u4eec\u5b9e\u9645\u4e0a\u662f 3 \u4e2a\u5171\u9762\u5411\u91cf<\/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>\u5224\u65ad\u4e0b\u5217\u56db\u4e2a\u5411\u91cf\u662f\u5426\u5171\u9762\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-10d37864162c9c1d2eae8f5b7c7df066_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{a}} = (2,1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" 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-0ab59c17a2058de83ef95ee9b7021751_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{b}} = (1,-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-1822f69d3738974e93084ea4c454d63f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{c}} = (-1,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" 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-f76c271b5fc0fe45fe9b2591346f083f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{d}} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u77e5\u9053\u56db\u4e2a\u5411\u91cf\u662f\u5426\u5171\u9762\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u6240\u6709\u5411\u91cf\u7ec4\u6210\u7684\u77e9\u9635\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-8384924c86edafd568505d5f80e1705d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} 2&amp;1&amp;1 \\\\[1.1ex] 1&amp;-1&amp;2 \\\\[1.1ex] -1&amp;0&amp;-1 \\\\[1.1ex] 3&amp;1&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"164\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u6240\u8ff0\u77e9\u9635\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-2778435c7f53952adf072419af8b268c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2&amp;1&amp;1 \\\\[1.1ex] 1&amp;-1&amp;2 \\\\[1.1ex] -1&amp;0&amp;-1 \\end{vmatrix}=0 \\quad  \\begin{vmatrix} 2&amp;1&amp;1 \\\\[1.1ex] 1&amp;-1&amp;2 \\\\[1.1ex]3&amp;1&amp;2\\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"280\" 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-82f278494a221879cc86da92ab4378c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2&amp;1&amp;1 \\\\[1.1ex] -1&amp;0&amp;-1 \\\\[1.1ex] 3&amp;1&amp;2\\end{vmatrix}=0 \\quad \\begin{vmatrix} 1&amp;-1&amp;2 \\\\[1.1ex] -1&amp;0&amp;-1 \\\\[1.1ex] 3&amp;1&amp;2\\end{vmatrix}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"294\" 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-889142ac348173dd6c838633007f2d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2&amp;1 \\\\[1.1ex] 1&amp;-1\\end{vmatrix}= -3\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"136\" 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 class=\"has-text-align-left\">\u6240\u6709\u5411\u91cf\u7ec4\u6210\u7684\u77e9\u9635\u7684\u79e9\u7b49\u4e8e2\uff0c\u56e0\u6b64<strong>4\u4e2a\u5411\u91cf\u5171\u9762<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f7f\u5f97\u4ee5\u4e0b 4 \u70b9\u5171\u9762\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-9483cca4fc2a94923b7c72ed89fc2d5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-a5b113e265916c03a6de0547cfeb380b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(2,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" 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-add9ad10fb8badd9de84f8ad1dcfe38d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(0,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-8d5054a3ce659090916cda61b74f60bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(3,2,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u56db\u4e2a\u70b9\u5171\u9762\uff0c\u7531\u5b83\u4eec\u786e\u5b9a\u7684\u5411\u91cf\u5fc5\u987b\u5171\u9762\u3002\u56e0\u6b64\u6211\u4eec\u8ba1\u7b97\u8fd9\u4e9b\u5411\u91cf\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-996a90c58f67665e4a68e9dd4de6c718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (2,1,2)-(3,1,4) = (-1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae552981d5729c931f5bbb26c133ecc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C- A = (0,-1,3)-(3,1,4) = (-3,-2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"392\" 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-91aec8ed49541d8c2d8ca0b3b1f8a20d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD} = D- A = (3,2,k)-(3,1,4) = (0,1,k-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"371\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u5411\u91cf\u77e9\u9635\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-c3d801efcf5b56dd858890720797d6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} -1&amp;0&amp;-2 \\\\[1.1ex] -3&amp;-2&amp;-1 \\\\[1.1ex] 0&amp;1&amp;k-4\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"181\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u6240\u5f97\u5411\u91cf\u5171\u9762\uff0c\u77e9\u9635\u7684\u79e9\u5fc5\u987b\u4e3a 2\u3002\u56e0\u6b64\uff0c\u6574\u4e2a 3&#215;3 \u77e9\u9635\u7684\u884c\u5217\u5f0f\u5fc5\u987b\u4e3a 0\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-bb7d3b31c10096d100843d781a85b621_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -1&amp;0&amp;-2 \\\\[1.1ex] -3&amp;-2&amp;-1 \\\\[1.1ex] 0&amp;1&amp;k-4\\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"160\" 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-b265559f1f5505b8c40a89f0d69f0c10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2k-3 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u6211\u4eec\u89e3\u51b3\u4e86\u672a\u77e5\u7684\u95ee\u9898<\/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-7cf6d2c84f82625cb8a795ee1394251f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" 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-f79b9d3960668149408038b9cb1d1e0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k =3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-e67be6e218d206fe735f54a6125b3d2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k =}\\mathbf{\\cfrac{3}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u5171\u9762\u5411\u91cf\u4ee5\u53ca\u5982\u4f55\u5224\u65ad 2\u30013\u30014 \u6216\u66f4\u591a\u5411\u91cf\u662f\u5426\u5171\u9762\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u5171\u9762\u5411 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e5%90%91%e9%87%8f\/\"> <span class=\"screen-reader-text\">\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u5411\u91cf<\/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":[21],"tags":[],"class_list":["post-258","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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