{"id":220,"date":"2023-07-11T03:30:24","date_gmt":"2023-07-11T03:30:24","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e7%9f%a2%e9%87%8f%e6%96%b9%e7%a8%8b%e7%9a%84%e5%85%ac%e5%bc%8f\/"},"modified":"2023-07-11T03:30:24","modified_gmt":"2023-07-11T03:30:24","slug":"%e7%9b%b4%e7%ba%bf%e7%9f%a2%e9%87%8f%e6%96%b9%e7%a8%8b%e7%9a%84%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e7%9f%a2%e9%87%8f%e6%96%b9%e7%a8%8b%e7%9a%84%e5%85%ac%e5%bc%8f\/","title":{"rendered":"\u76f4\u7ebf\u7684\u5411\u91cf\u65b9\u7a0b"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u60a8\u8fd8\u5c06\u53d1\u73b0\u5982\u4f55\u4ece\u77e2\u91cf\u65b9\u7a0b\u83b7\u5f97\u76f4\u7ebf\u7684\u70b9\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-ecuacion-vectorial-de-la-recta\"><\/span>\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u76f4\u7ebf\u7684\u6570\u5b66\u5b9a\u4e49\u662f\u4e00\u7ec4\u8fde\u7eed\u7684\u70b9\uff0c\u8fd9\u4e9b\u70b9\u4ee5\u76f8\u540c\u7684\u65b9\u5411\u8868\u793a\uff0c\u6ca1\u6709\u66f2\u7ebf\u6216\u89d2\u5ea6\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u56e0\u6b64\uff0c<strong>\u7ebf\u5411\u91cf\u65b9\u7a0b<\/strong>\u662f\u4e00\u79cd\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u4efb\u4f55\u7ebf\u7684\u65b9\u6cd5\u3002\u5e76\u4e14\uff0c\u4e3a\u6b64\uff0c\u6240\u9700\u8981\u7684\u53ea\u662f\u5c5e\u4e8e\u8be5\u7ebf\u7684\u4e00\u4e2a\u70b9\u548c\u8be5\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-la-ecuacion-vectorial-de-la-recta\"><\/span>\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u662f\u7684<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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>\u662f\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c5e\u4e8e\u53f3\u8fb9\u7684\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-798c10bf651dde568bef6722fc25cef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2) \\qquad P(P_1,P_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"><strong>\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b<\/strong>\u7684\u516c\u5f0f\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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px;\">\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" 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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u7ebf\u4e0a\u4efb\u610f\u70b9\u7684\u7b1b\u5361\u5c14\u5750\u6807\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/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-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u5c5e\u4e8e\u7ebf\u7684\u5df2\u77e5\u70b9\u7684\u5750\u6807\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/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-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u76f4\u7ebf\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u4e00\u4e2a\u6807\u91cf\uff08\u5b9e\u6570\uff09\uff0c\u5176\u503c\u53d6\u51b3\u4e8e\u7ebf\u4e0a\u7684\u6bcf\u4e2a\u70b9\u3002 <\/li>\n<\/ul>\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-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equations-de-la-droite-1.webp\" alt=\"\u7b2c 4 \u884c\u7684\u5411\u91cf\u65b9\u7a0b\" class=\"wp-image-1304\" width=\"281\" height=\"268\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5b83\u662f\u5e73\u9762\u4e2d\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5f53\u4f7f\u7528 2 \u4e2a\u5750\u6807\uff08\u5728 R2 \u4e2d\uff09\u7684\u70b9\u548c\u77e2\u91cf\u65f6\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u5728\u7a7a\u95f4\u4e2d\uff08\u5728 R3 \u4e2d\uff09\u8fdb\u884c\u8ba1\u7b97\uff0c\u6211\u4eec\u5c31\u5fc5\u987b\u5728\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u989d\u5916\u7684\u5206\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-3ef53596406b2fe36258a0421c91336b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_1,P_2,P_3)+t\\cdot (\\text{v}_1,\\text{v}_2,\\text{v}_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u9664\u4e86\u77e2\u91cf\u65b9\u7a0b\u4e4b\u5916\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\u53ef\u4ee5\u89e3\u6790\u5730\u8868\u8fbe\u76f4\u7ebf\uff1a\u53c2\u6570\u65b9\u7a0b\u3001\u8fde\u7eed\u65b9\u7a0b\u3001\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u3001\u663e\u5f0f\u65b9\u7a0b\u548c\u76f4\u7ebf\u7684\u70b9\u659c\u7387\u65b9\u7a0b\u3002\u60a8\u53ef\u4ee5\u5728\u6b64\u94fe\u63a5<a href=\"https:\/\/mathority.org\/cn\/\u76f4\u7ebf\u65b9\u7a0b-\u6240\u6709\u516c\u5f0f-\u793a\u4f8b-\u5df2\u89e3\u7b54-\u7ec3\u4e60\/\">\u7684\u884c\u4e2d\u67e5\u770b\u6240\u6709\u7c7b\u578b\u7684\u65b9\u7a0b<\/a>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-ecuacion-vectorial-de-la-recta\"><\/span>\u5982\u4f55\u6c42\u76f4\u7ebf\u5411\u91cf\u65b9\u7a0b\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u786e\u5b9a\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\uff1a<\/p>\n<ul>\n<li>\u5199\u51fa\u7ecf\u8fc7\u8be5\u70b9\u7684\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5e76\u4e14\u6709<\/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>\u4f5c\u4e3a\u5f15\u5bfc\u5411\u91cf\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-c4f245fcb7cc0cea584213b379d0cc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (1,2) \\qquad P(3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u627e\u5230\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\uff0c\u53ea\u9700\u5e94\u7528\u5176\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-d4d382959b5006597c30376b200d167f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,0)+t\\cdot (1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"obtener-puntos-a-partir-de-la-ecuacion-vectorial-de-la-recta\"><\/span>\u4ece\u76f4\u7ebf\u7684\u5411\u91cf\u65b9\u7a0b\u4e2d\u83b7\u53d6\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u627e\u5230\u4e86\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\uff0c\u5c31\u5f88\u5bb9\u6613\u8ba1\u7b97\u51fa\u76f4\u7ebf\u7ecf\u8fc7\u7684\u70b9\u3002\u8981\u786e\u5b9a\u7ebf\u4e0a\u7684\u70b9<strong>\uff0c\u53ea\u9700\u4e3a\u53c2\u6570\u6307\u5b9a\u4e00\u4e2a\u503c\u5373\u53ef<\/strong><\/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-50d6971192a73f12b183dbddd7c75197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{t}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u76f4\u7ebf\u7684\u5411\u91cf\u65b9\u7a0b\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u7ed9\u5b9a\u4ee5\u4e0b\u76f4\u7ebf\u5411\u91cf\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd6dd1a3c3a001280f7fc7d94713c2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(1,-1)+t\\cdot (2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u66f4\u6362\u5373\u53ef\u5f97\u5206<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4efb\u610f\u6570\u5b57\uff0c\u4f8b\u5982<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-81a04a05d8ea6730567685bff8148959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+1\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(2,3) \\\\[2ex] &amp; = (1+2 \\ , -1+3) \\\\[2ex] &amp; = \\bm{(3,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u7ebf\u4e0a\u7684\u53e6\u4e00\u4e2a\u70b9\u7ed9\u51fa\u672a\u77e5\u6570<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0d\u540c\u7684\u6570\u5b57\uff0c\u4f8b\u5982<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-70cfec547c993eddfea11d50bef03bae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+2\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(4,6) \\\\[2ex] &amp; = (1+4 \\ , -1+6) \\\\[2ex] &amp; = \\bm{(5,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u76f4\u7ebf\u4e0a\u65e0\u7a77\u591a\u4e2a\u70b9\uff0c\u56e0\u4e3a\u53d8\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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u53ef\u4ee5\u53d6\u65e0\u9650\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-vectorial-de-la-recta\"><\/span>\u89e3\u51b3\u4e86\u76f4\u7ebf\u77e2\u91cf\u65b9\u7a0b\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6c42\u901a\u8fc7\u8be5\u70b9\u7684\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5176\u65b9\u5411\u5411\u91cf\u4e3a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80c361259467f8dee47e246c764ef897_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-b5adb01b1c1b8426314e6158a3ad6ff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,3) \\qquad \\vv{\\text{v}}=(4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"188\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\uff0c\u53ea\u9700\u5e94\u7528\u5176\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u8ba1\u7b97\u4e0a\u4e00\u4e2a\u95ee\u9898\u7684\u76f4\u7ebf\u4e0a\u7684\u4e09\u4e2a\u70b9\u3002 <\/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\u4ece\u77e2\u91cf\u65b9\u7a0b\u63cf\u8ff0\u7684\u76f4\u7ebf\u4e0a\u83b7\u53d6\u70b9\uff0c\u5fc5\u987b\u7ed9\u53c2\u6570\u8d4b\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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0a\u4e00\u9898\u8ba1\u7b97\u51fa\u7684\u5411\u91cf\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u8ba1\u7b97\u4e00\u4e2a\u70b9\uff0c\u6211\u4eec\u66ff\u6362\u672a\u77e5\u6570<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f8b\u5982\u901a\u8fc7<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-36452411cca47b72db95b2876b03f69d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+1\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (4,-2) \\\\[2ex] &amp; = (-1+4 \\ , 3-2) \\\\[2ex] &amp; = \\bm{(3,1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u627e\u5230\u7b2c\u4e8c\u70b9\uff0c\u6211\u4eec\u7ed9\u51fa<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f8b\u5982\u7684\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-5a5fe3c08ab62695f62cf76df97aac2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+2\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (8,-4) \\\\[2ex] &amp; = (-1+8 \\ , 3-4) \\\\[2ex] &amp; = \\bm{(7,-1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u8d4b\u503c\u5f97\u5230\u7b2c\u4e09\u70b9<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7684\u4ef7\u503c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-063c366f7c1d1f7a8a92c459c8c495d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=3:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-9710aef8527fc6c53d21109ea01a1b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+3\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (12,-6) \\\\[2ex] &amp; = (-1+12 \\ , 3-6) \\\\[2ex] &amp; = \\bm{(11,-3)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u60a8\u53ef\u80fd\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u5206\u6570\uff0c\u56e0\u4e3a\u8fd9\u53d6\u51b3\u4e8e\u60a8\u8d4b\u4e88\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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f46\u5982\u679c\u60a8\u9075\u5faa\u76f8\u540c\u7684\u7a0b\u5e8f\uff0c\u4e00\u5207\u90fd\u4f1a\u597d\u8d77\u6765\u7684\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>\u6216\u8005\u8bf4\u4e24\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39e1ccbebf7e7d41e0c9bc87567a83c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,1) \\qquad B(3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6c42\u901a\u8fc7\u8fd9\u4e24\u70b9\u7684\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\u3002 <\/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\u6211\u4eec\u6ca1\u6709\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u627e\u5230\u5b83\u7684\u65b9\u5411\u5411\u91cf\uff0c\u7136\u540e\u627e\u5230\u76f4\u7ebf\u7684\u65b9\u7a0b\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8981\u627e\u5230\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u7531\u4e24\u4e2a\u7ed9\u5b9a\u70b9\u5b9a\u4e49\u7684\u5411\u91cf\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ef2698c8dcca35e09a5fbbb3c07bdcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A= (3,-2)- (5,1) = (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6839\u636e\u7ed9\u5b9a\u7684\u70b9\u4e4b\u4e00\u548c\u516c\u5f0f\u786e\u5b9a\u5176\u5411\u91cf\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-68960ac44d082e7f07e54f954e16ac41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(5,1)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5c06\u53e6\u4e00\u4e2a\u7ed9\u5b9a\u70b9\u4ee3\u5165\u516c\u5f0f\u5f97\u51fa\u7684\u65b9\u7a0b\u4e5f\u662f\u6709\u6548\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-a3931a59d4987a867d7e380fe782df9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,-2)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"224\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u76f4\u7ebf\u7684\u77e2\u91cf\u65b9\u7a0b\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u60a8\u8fd8\u5c06\u53d1\u73b0\u5982 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e7%9f%a2%e9%87%8f%e6%96%b9%e7%a8%8b%e7%9a%84%e5%85%ac%e5%bc%8f\/\"> <span class=\"screen-reader-text\">\u76f4\u7ebf\u7684\u5411\u91cf\u65b9\u7a0b<\/span> \u67e5\u770b\u5168\u6587 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