{"id":209,"date":"2023-07-11T21:43:45","date_gmt":"2023-07-11T21:43:45","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e4%b8%8e%e6%a0%87%e9%87%8f%e5%ae%9e%e6%95%b0%e7%9a%84%e4%b9%98%e7%a7%af\/"},"modified":"2023-07-11T21:43:45","modified_gmt":"2023-07-11T21:43:45","slug":"%e5%90%91%e9%87%8f%e4%b8%8e%e6%a0%87%e9%87%8f%e5%ae%9e%e6%95%b0%e7%9a%84%e4%b9%98%e7%a7%af","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e4%b8%8e%e6%a0%87%e9%87%8f%e5%ae%9e%e6%95%b0%e7%9a%84%e4%b9%98%e7%a7%af\/","title":{"rendered":"\u5411\u91cf\u4e58\u4ee5\u6570\u5b57"},"content":{"rendered":"<p>\u672c\u9875\u8bf4\u660e\u5982\u4f55\u4ee5\u6570\u5b57\u548c\u56fe\u5f62\u65b9\u5f0f\u5c06\u5411\u91cf\u4e58\u4ee5\u5b9e\u6570\uff08\u6216\u6807\u91cf\uff09\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u5411\u91cf\u4e0e\u6807\u91cf\u4e58\u79ef\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u8fd8\u89e3\u91ca\u4e86\u8fd9\u79cd\u5411\u91cf\u8fd0\u7b97\u7684\u6027\u8d28\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-multiplica-un-vector-por-un-numero-real\"><\/span>\u5982\u4f55\u5c06\u5411\u91cf\u4e58\u4ee5\u5b9e\u6570\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u8981\u4ee5\u6570\u503c\u65b9\u5f0f\u8ba1\u7b97\u5411\u91cf\u548c\u6570\u5b57\uff08\u6216\u6807\u91cf\uff09\u7684\u4e58\u79ef\uff0c\u5411\u91cf\u7684\u6bcf\u4e2a\u5206\u91cf\u5fc5\u987b\u4e58\u4ee5\u6570\u5b57\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-d4b2f8c9cdb09377a66fbce8392c30ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -6px;\"><\/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-abb3b5391be9c0e4d871ff45367ca838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\\cdot \\vv{\\text{u}} =(k\\cdot \\text{u}_x \\ , \\ k\\cdot \\text{u}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u5411\u91cf\u4e58\u4ee5\u6570\u5b57\u7684\u7ed3\u679c\u4f1a\u4ea7\u751f\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\u7684\u65b0\u5411\u91cf\uff1a<\/p>\n<ul style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u5411\u91cf\u4e0e\u6807\u91cf\u76f8\u4e58\u7684\u7ed3\u679c\u4f1a\u4ea7\u751f\u4e00\u4e2a\u4e0e\u539f\u59cb\u5411\u91cf\u65b9\u5411\u76f8\u540c\u7684\u65b0\u5411\u91cf\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u6b64\u5916\uff0c\u5982\u679c\u6570\u5b57\u4e3a\u6b63\uff0c\u5219\u65b0\u5411\u91cf\u5c06\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u5426\u5219\uff0c\u5982\u679c\u8be5\u6570\u4e3a\u8d1f\u6570\uff0c\u5219\u5176\u542b\u4e49\u76f8\u53cd\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u7ed3\u679c\u5411\u91cf\u7684\u5927\u5c0f\u7b49\u4e8e\u539f\u59cb\u5411\u91cf\u7684\u5927\u5c0f\u4e58\u4ee5\u6807\u91cf\u3002<\/span><\/li>\n<\/ul>\n<p>\u5728\u4e0b\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u65e0\u8bba\u6807\u91cf\u7684\u7b26\u53f7\u5982\u4f55\uff0c\u5982\u4f55\u4fdd\u6301\u77e2\u91cf\u7684\u65b9\u5411\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5411\u91cf\u7684\u65b9\u5411\u53d6\u51b3\u4e8e\u5b83\u76f8\u4e58\u7684\u6570\u5b57\u7684\u7b26\u53f7\u3002 <\/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\/multiplication-ou-produit-dun-nombre-ou-dun-scalaire-par-un-vecteur.webp\" alt=\"\u6570\u5b57\u6216\u6807\u91cf\u4e0e\u5411\u91cf\u7684\u4e58\u6cd5\u6216\u4e58\u79ef\" class=\"wp-image-283\" width=\"305\" height=\"206\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b64\u5916\uff0c\u5728\u4e0b\u56fe\u4e2d\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u5230\uff0c\u6240\u5f97\u4e58\u79ef\u5411\u91cf\u7684\u5927\u5c0f\u7b49\u4e8e\u539f\u59cb\u5411\u91cf\u7684\u5927\u5c0f\u4e58\u4ee5\u6807\u91cf\u3002 <\/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\/numero-de-produit-de-multiplication-de-module-par-vecteur.webp\" alt=\"\u6570\u5b57\u4e0e\u5411\u91cf\u7684\u4e58\u6cd5\u6216\u4e58\u79ef\u7684\u6a21\u5982\u4f55\u6f14\u5316\uff1f\" class=\"wp-image-290\" width=\"255\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u663e\u7136\uff0c\u5982\u679c\u6211\u4eec\u5c06\u5411\u91cf\u4e58\u4ee5\u5927\u4e8e 1 \u7684\u6570\u5b57\uff0c\u7ed3\u679c\u5c06\u662f\u4e00\u4e2a\u957f\u5ea6\u66f4\u5927\uff08\u6a21\u6570\u66f4\u5927\uff09\u7684\u5411\u91cf\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6211\u4eec\u5c06\u5411\u91cf\u4e58\u4ee5\u5c0f\u4e8e 1 \u7684\u6570\uff0c\u5219\u7ed3\u679c\u662f\u957f\u5ea6\u8f83\u77ed\uff08\u6a21\u6570\u8f83\u5c0f\uff09\u7684\u5411\u91cf\u3002<\/p>\n<p><strong>\u6ce8\u610f\uff1a<\/strong>\u4e0d\u8981\u5c06\u5411\u91cf\u548c <a href=\"https:\/\/mathority.org\/cn\/\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u6807\u91cf\u79ef-\u5df2\u89e3\u51b3\u7684\u793a\u4f8b\u7ec3\u4e60\/\">\u6807\u91cf\u7684\u4e58\u79ef\u4e0e\u5411\u91cf\u7684\u70b9\u79ef<\/a>\u6df7\u6dc6\u3002\u867d\u7136\u5b83\u4eec\u7684\u540d\u5b57\u76f8\u4f3c\uff0c\u4f46\u5b83\u4eec\u662f\u4e24\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u6982\u5ff5\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-producto-de-un-vector-por-un-escalar\"><\/span>\u5411\u91cf\u4e0e\u6807\u91cf\u7684\u4e58\u79ef\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e00\u4e2a\u6570\u503c\u793a\u4f8b\uff0c\u8bf4\u660e\u5982\u4f55\u8ba1\u7b97\u5411\u91cf\u548c\u6570\u5b57\u7684\u4e58\u79ef\uff1a<\/p>\n<ul>\n<li>\u5c06\u4ee5\u4e0b\u5411\u91cf\u4e58\u4ee5 4\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-0a3b02659b94a332ef3cd2cc62769d94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} =(2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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-998ae86a47fde44f6006a0744f03c562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{\\text{u}} =(4 \\cdot 2 \\ , \\ 4 \\cdot (-3)) = \\bm{(8,-12)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"263\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u8fd9\u79cd\u7c7b\u578b\u7684\u5411\u91cf\u8fd0\u7b97\u5e76\u4e0d\u662f\u5f88\u590d\u6742\uff0c\u56e0\u4e3a\u60a8\u4e0d\u5fc5\u8fdb\u884c\u5927\u91cf\u8ba1\u7b97\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8fd8\u6709\u66f4\u590d\u6742\u7684\u5411\u91cf\u8fd0\u7b97\uff0c\u4f8b\u5982\u5411\u91cf\u52a0\u6cd5\u548c\u5411\u91cf\u51cf\u6cd5\u3002\u5982\u679c\u60a8\u5df2\u7ecf\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u5411\u91cf\u548c\u6807\u91cf\u7684\u4e58\u79ef\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u8fdb\u5165\u4e0b\u4e00\u4e2a\u7ea7\u522b\uff0c\u770b\u770b\u5982\u4f55\u6c42\u89e3 <a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u4e4b\u548c-\u4ee5\u56fe\u5f62\u65b9\u5f0f\u6570\u503c\u6c42\u89e3-\u793a\u4f8b-\u7ec3\u4e60-\u6dfb\u52a0\/\">\u5411\u91cf\u52a0\u6cd5<\/a>\u548c<a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u51cf\u6cd5-\u6570\u5b57\u56fe\u5f62-\u4f8b\u5b50-\u89e3\u51b3\u7ec3\u4e60-\u51cf\u6cd5\/\">\u5411\u91cf\u51cf\u6cd5<\/a>\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u8fd0\u7b97\u6709\u4e9b\u56f0\u96be\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u4eec\u88ab\u4f7f\u7528\u5f97\u66f4\u591a\uff08\u5b83\u4eec\u66f4\u91cd\u8981\uff09\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-multiplicacion-de-un-vector-por-un-numero\"><\/span>\u5411\u91cf\u4e58\u4ee5\u6570\u5b57\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5411\u91cf\u548c\u6570\u5b57\u7684\u4e58\u79ef\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n<ul>\n<li><strong>\u7ed3\u5408\u6027<\/strong>\uff1a\u5f53\u5411\u91cf\u4e58\u4ee5\u591a\u4e2a\u6570\u65f6\uff0c\u4e58\u6cd5\u7684\u987a\u5e8f\u5e76\u4e0d\u91cd\u8981\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-a7cc3b0e34695b9960f32199046e868e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (k' \\cdot \\vv{\\text{u}}) =(k\\cdot k') \\cdot \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5173\u4e8e\u5411\u91cf\u52a0\u6cd5\u548c\u51cf\u6cd5\u7684<strong>\u5206\u914d\u5f8b<\/strong>\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-a8b55a3b25ad66154d6e8bb18fc70da7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}+  \\vv{\\text{v}})=k\\cdot \\vv{\\text{u}} + k\\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" 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-086f60151d160ac3b6d4f5add59434b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}- \\vv{\\text{v}})=k\\cdot \\vv{\\text{u}} - k\\cdot \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5173\u4e8e\u6807\u91cf\u76f8\u52a0\u7684<strong>\u5206\u914d\u6027\u8d28<\/strong>\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-7354955effb7b59f41793537f4517851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(k+k') \\cdot \\vv{\\text{u}} =k\\cdot \\vv{\\text{u}} + k'\\cdot \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u4e2d\u6027\u5143\u7d20<\/strong>\uff1a\u663e\u7136\uff0c\u4efb\u4f55\u5411\u91cf\u4e58\u4ee51\u90fd\u4f1a\u5f97\u5230\u5411\u91cf\u672c\u8eab\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-154c7987de1e55e762dcf229eae9fd23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot \\vv{\\text{u}} = \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-multiplicacion-de-un-vector-por-un-escalar\"><\/span>\u89e3\u51b3\u4e86\u5411\u91cf\u4e0e\u6807\u91cf\u76f8\u4e58\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u89e3\u6790\u8ba1\u7b97\u4ee5\u4e0b\u5411\u91cf\u4e0e 3 \u7684\u4e58\u79ef\u7ed3\u679c\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-8b5a56f394f2b178a0175a53e6a55a1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(-2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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\u6c42\u4e58\u79ef\uff0c\u5fc5\u987b\u5c06\u5411\u91cf\u7684\u6bcf\u4e2a\u5750\u6807\u4e58\u4ee5 3\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-4e0b8a6167489c27e91bef24f222e3af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot \\vv{a}=(3\\cdot (-2), 3 \\cdot 5) = \\bm{(-6,15)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"250\" 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>\u5c06\u4ee5\u4e0b\u5411\u91cf\u4e58\u4ee5 6 \u5e76\u627e\u5230\u5176\u6a21\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-85db994a57a1325a456909a04efa2e23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(3,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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\">\u6211\u4eec\u9996\u5148\u5c06\u5411\u91cf\u4e58\u4ee5\u6807\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-7c6c6b2d9291528aff357e7e94daf221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot \\vv{a}=(6\\cdot 3, 6 \\cdot (-4)) = (18,-24)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6709\u4e24\u79cd\u65b9\u6cd5\u6765\u8ba1\u7b97\u6240\u83b7\u5f97\u7684\u5411\u91cf\u7684\u5927\u5c0f\u3002\u9996\u5148\u662f\u627e\u5230\u539f\u59cb\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u7136\u540e\u5c06\u5176\u4e58\u4ee5 6\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-7a7bc760b63c8efa2c36d2d49802000c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{a} \\rvert =\\sqrt{3^2+(-4)^2} = \\sqrt{25} =5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"229\" style=\"vertical-align: -6px;\"><\/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-32f0e3a2cb32142aa26a1fbb0f3bf9df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot \\lvert \\vv{a} \\rvert =6\\cdot 5 =\\bm{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b2c\u4e8c\u79cd\u65b9\u5f0f\u662f\u76f4\u63a5\u8ba1\u7b97\u76f8\u4e58\u5f97\u5230\u7684\u5411\u91cf\u7684\u5927\u5c0f\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-06f0793bfdae917904c47247b9b1f08f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert 6\\cdot \\vv{a} \\rvert =\\sqrt{18^2+(-24)^2} = \\sqrt{900} =\\bm{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"287\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8fd9\u4e24\u4e2a\u8fc7\u7a0b\u90fd\u8868\u660e\u7ed3\u679c\u4e0d\u4f9d\u8d56\u4e8e\u8ba1\u7b97\u6a21\u91cf\u7684\u65b9\u6cd5\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>\u4ece\u4ee5\u4e0b\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-cf8d63b14f91ee738fe5107ab2a05779_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a}=(4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ee5\u4ee3\u6570\u65b9\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u8fd0\u7b97\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-5557b66d322653674e2266800c73c958_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" 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-a2f511cc4014aae8cf90bef442f30bdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" 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-d09a188710cecb56283c4a2dea7a97e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2} \\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"33\" 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-7c4742e8a37f45e358d2e7740c5aadef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u63a5\u4e0b\u6765\u5224\u65ad\u5f97\u5230\u7684\u5411\u91cf\u662f\u5426\u4e0e\u539f\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u548c\u65b9\u5411\uff0c\u5e76\u6309\u7167\u4ece\u6700\u77ed\u5230\u6700\u957f\u7684\u987a\u5e8f\u6392\u5217\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\">\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u4e58\u6cd5\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-6b92c621a30ebf15a0628cba3e0f6be5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot \\vv{a}=(2\\cdot 4, 2 \\cdot (-1)) = (8,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" 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-71e1eb36b88b2ca47d69f0bfe4d1a33b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot \\vv{a}=(-3\\cdot 4, -3 \\cdot (-1)) = (-12,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" 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-d9866b27859b66475a36d182919ec4e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\cdot \\vv{a}=\\left(\\frac{1}{2}\\cdot 4, \\frac{1}{2} \\cdot (-1)\\right) = \\left(2,-\\frac{1}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"277\" style=\"vertical-align: -17px;\"><\/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-6904a22660dc2e21ab3f775e1453535c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\vv{a}=(4\\cdot 4, 4 \\cdot (-1)) = (16,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"250\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5411\u91cf\u4e58\u4ee5\u6b63\u6570\uff0c\u5176\u65b9\u5411\u548c\u65b9\u5411\u4e0e\u539f\u5411\u91cf\u76f8\u540c\u3002\u5411\u91cf\u4e58\u4ee5\u8d1f\u6570\u4e0e\u539f\u5411\u91cf\u65b9\u5411\u76f8\u540c\u4f46\u65b9\u5411\u76f8\u53cd\u3002<\/p>\n<p class=\"has-text-align-center\">\u540c\u65b9\u5411\u548c\u540c\u65b9\u5411\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-50dd29950a1b957a78493d3de5b4bf5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2\\vv{a}, \\ 4\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"50\" style=\"vertical-align: -4px;\"><\/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-9fac7295c812fa36c4fcba97e316b5f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"20\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\u65b9\u5411\u76f8\u540c\u4f46\u542b\u4e49\u4e0d\u540c\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-d1b95a4d066d0dd0da8cdf0373d19c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\vv{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5fc5\u987b\u6839\u636e\u5411\u91cf\u7684\u957f\u5ea6\u6216\u7b49\u6548\u7684\u6a21\u6570\u5bf9\u5411\u91cf\u8fdb\u884c\u6392\u5e8f\u3002\u6700\u957f\u957f\u5ea6\uff08\u6216\u6700\u5927\u6a21\u5757\uff09\u7684\u5411\u91cf\u5c06\u662f\u4e58\u4ee5\u8f83\u5927\u6570\uff08\u7edd\u5bf9\u503c\uff09\u7684\u5411\u91cf\uff0c\u6700\u77ed\u957f\u5ea6\uff08\u6216\u6700\u5c0f\u6a21\u5757\uff09\u7684\u5411\u91cf\u5c06\u662f\u5df2\u4e58\u4ee5\u8f83\u5c0f\u6570\u7684\u5411\u91cf\u6570\u91cf\uff08\u7edd\u5bf9\u503c\uff09\u3002\u6240\u4ee5\u957f\u5ea6\u7684\u987a\u5e8f\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-b1e7cf58774569c9f128f49948c9fead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} \\displaystyle\\frac{1}{2}\\vv{a}\\end{vmatrix} <\\lvert 2\\vv{a}\\rvert < \\lvert -3\\vv{a}\\rvert < \\lvert 4\\vv{a}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"199\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u6ce8\u610f\uff0c\u957f\u5ea6\u6216\u6a21\u6570\u4e0d\u53d6\u51b3\u4e8e\u76f8\u4e58\u6807\u91cf\u7684\u7b26\u53f7\uff0c\u56e0\u4e3a\u77e2\u91cf\u7684\u65b9\u5411\u4e0d\u4f1a\u4fee\u6539\u5176\u6a21\u6570\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>\u8003\u8651\u4ee5\u4e0b\u4e24\u4e2a\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-740cd5f2540cb57342f82c58e1076cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a} =(7,-2) \\qquad \\vv{b} =(-3,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"205\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\u5982\u4e0b\u8fd0\u7b97\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-5abd316200fbcf062072dfdf51266cda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\vv{a} - 3 \\vv{b}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" 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\">\u6211\u4eec\u9996\u5148\u89e3\u51b3\u5411\u91cf\u4e0e\u6570\u5b57\u7684\u4e58\u6cd5\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-08a07c35741b9e7427990abb5bb89ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot \\vv{a} - 3 \\cdot \\vv{b}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-5fa31543d7c2a129c47b030cfa5fc4e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot (7,-2) - 3 \\cdot(-3,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" 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-d7624e801962ac397ca316243c4e3420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(14,-4) - (-9,15)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u51cf\u53bb\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-72660b240eab9459d0b0aefb1d10d728_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(14-(-9),-4-15)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" 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-fe8b5f018f4a24a925bfce0c2c997dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(23,-19)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" 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\u4e605<\/h3>\n<p>\u6267\u884c\u4ee5\u4e0b\u5411\u91cf\u4e0e\u6807\u91cf\u7684\u4e58\u6cd5\u5e76\u7ed8\u5236\u7ed3\u679c\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-b1c2fa6e2c114b3bbce76ca987020ad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" 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-1adddd551d57bc95b951c6573080090a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot (-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" 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-33be3689306562b8a4ae74d0970fc1f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot (2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" 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-bd3d3bba47ccc84d7616e38ca863b22d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{2}\\cdot (-2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"76\" 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-8fe6e18de5ed93f74fa207a3f9ecc2c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -\\frac{1}{2}\\cdot (8,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"77\" style=\"vertical-align: -12px;\"><\/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\">\u6211\u4eec\u9996\u5148\u5c06\u5411\u91cf\u4e58\u4ee5\u5b9e\u6807\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-6846258bc5f69aaea3f86991095d3199_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (1,2) = (2\\cdot 1,2\\cdot 2)=\\bm{(2,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"230\" 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-605e263cab7e34f01290372f0e2666c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\cdot (-1,1) = (-3\\cdot (-1),-3\\cdot 1)=\\bm{(3,-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"325\" 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-b8b4cf7b606673d72ae9cdd0004f0757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot (2,1) = (4\\cdot 2,4\\cdot 1)=\\bm{(8,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"230\" 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-51454cc5c3239bb4552918b1a693b499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{2}\\cdot (-2,4)= \\left(\\frac{3}{2}\\cdot (-2), \\frac{3}{2}\\cdot 4 \\right) = \\bm{(-3,6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"307\" style=\"vertical-align: -17px;\"><\/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-8fbbfff835499e861d11de5da6714d10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -\\frac{1}{2}\\cdot (8,6)= \\left(-\\frac{1}{2}\\cdot 8, -\\frac{1}{2}\\cdot 6 \\right) = \\bm{(-4,-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"322\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u5c06\u5b83\u4eec\u8868\u793a\u5728\u56fe\u4e2d\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\/exercices-et-problemes-resolus-de-multiplication-dun-vecteur-par-un-nombre.webp\" alt=\"\u7ec3\u4e60\u5e76\u89e3\u51b3\u5411\u91cf\u4e58\u4ee5\u6570\u5b57\u7684\u95ee\u9898\" class=\"wp-image-327\" width=\"469\" height=\"370\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9875\u8bf4\u660e\u5982\u4f55\u4ee5\u6570\u5b57\u548c\u56fe\u5f62\u65b9\u5f0f\u5c06\u5411\u91cf\u4e58\u4ee5\u5b9e\u6570\uff08\u6216\u6807\u91cf\uff09\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u5411\u91cf\u4e0e\u6807\u91cf\u4e58\u79ef\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6700\u540e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e4%b8%8e%e6%a0%87%e9%87%8f%e5%ae%9e%e6%95%b0%e7%9a%84%e4%b9%98%e7%a7%af\/\"> <span class=\"screen-reader-text\">\u5411\u91cf\u4e58\u4ee5\u6570\u5b57<\/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-209","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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