{"id":219,"date":"2023-07-11T05:03:07","date_gmt":"2023-07-11T05:03:07","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%ad%a3%e4%ba%a4%e5%9e%82%e7%9b%b4%e5%90%91%e9%87%8f\/"},"modified":"2023-07-11T05:03:07","modified_gmt":"2023-07-11T05:03:07","slug":"%e6%ad%a3%e4%ba%a4%e5%9e%82%e7%9b%b4%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%ad%a3%e4%ba%a4%e5%9e%82%e7%9b%b4%e5%90%91%e9%87%8f\/","title":{"rendered":"\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5782\u76f4\uff08\u6216\u6b63\u4ea4\uff09\u5411\u91cf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u4eec\u662f\u4ec0\u4e48\uff0c\u5f53\u4e24\u4e2a\u5411\u91cf\u6b63\u4ea4\u65f6\uff0c\u5982\u4f55\u627e\u5230\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u5411\u91cf\uff0c\u5782\u76f4\u5411\u91cf\u7684\u5c5e\u6027\uff0c&#8230;\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf\u7684\u51e0\u4e2a\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-vectores-perpendiculares-u-ortogonales\"><\/span>\u4ec0\u4e48\u662f\u4e24\u4e2a\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\">\u5728\u6570\u5b66\u4e2d\uff0c\u5f53\u4e24\u4e2a\u5411\u91cf\u5f7c\u6b64\u5f62\u6210\u76f4\u89d2 (90\u00b0) \u65f6\uff0c\u5b83\u4eec\u5c31\u662f<strong>\u6b63\u4ea4<\/strong>\uff08\u6216<strong>\u5782\u76f4<\/strong>\uff09\u3002<\/p>\n<p>\u5728\u4e0b\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u4e24\u4e2a\u5782\u76f4\u7684\u5411\u91cf\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteurs-perpendiculaires-ou-orthogonaux.webp\" alt=\"\u5f53\u4e24\u4e2a\u5411\u91cf\u88ab\u79f0\u4e3a\u5782\u76f4\u6216\u6b63\u4ea4\u65f6\" class=\"wp-image-1263\" width=\"195\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u5782\u76f4\u5ea6\u4ec5\u53d6\u51b3\u4e8e\u5b83\u4eec\u7684\u65b9\u5411\uff0c\u800c\u4e0d\u53d6\u51b3\u4e8e\u5b83\u4eec\u7684\u6a21\uff08\u6216\u5927\u5c0f\uff09\uff0c\u6216\u8005\u663e\u7136\uff0c\u53d6\u51b3\u4e8e\u5b83\u4eec\u7684\u65b9\u5411\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u6210 90 \u5ea6\u89d2\uff0c\u5219\u65e0\u8bba\u5b83\u4eec\u7684\u957f\u5ea6\u662f\u5426\u76f8\u540c\uff0c\u5b83\u4eec\u90fd\u662f\u5782\u76f4\u7684\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-vectores-son-ortogonales-o-perpendiculares\"><\/span>\u5982\u4f55\u77e5\u9053\u4e24\u4e2a\u5411\u91cf\u662f\u6b63\u4ea4\u8fd8\u662f\u5782\u76f4\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u521a\u521a\u770b\u5230\u7684\uff0c\u4ece\u56fe\u5f62\u4e0a\u5f88\u5bb9\u6613\u770b\u51fa\u4e24\u4e2a\u5411\u91cf\u662f\u5426\u5782\u76f4\u3002\u4f46\u662f\uff0c\u60a8\u4e5f\u53ef\u4ee5\u786e\u5b9a\u4e24\u4e2a\u5411\u91cf\u662f\u5426\u6b63\u4ea4\uff0c\u800c\u65e0\u9700\u7ed8\u5236\u5b83\u4eec\uff1a<\/p>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\">\u4ece\u6570\u503c\u4e0a\u6765\u8bf4\uff0c\u5f53\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u4e3a\u96f6 (0) \u65f6\uff0c\u5b83\u4eec\u5c31\u662f<strong>\u6b63\u4ea4<\/strong>\u6216<strong>\u5782\u76f4\u7684<\/strong>\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u663e\u793a\u4ee5\u4e0b\u4e24\u4e2a\u5411\u91cf\u662f\u5782\u76f4\u7684\uff0c\u800c\u65e0\u9700\u7ed8\u5236\u5b83\u4eec\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-54fd3ebc4e192bb4cbd2fbd0bcc42fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(3,2) \\qquad\\vv{\\text{v}}=(-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u68c0\u67e5\u8fd9\u4e9b\u5411\u91cf\u662f\u5426\u5782\u76f4\uff08\u6216\u6b63\u4ea4\uff09\uff0c\u6211\u4eec\u5e94\u7528 <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\u79ef\u516c\u5f0f<\/a>\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73197e497b384965865651ffea4caea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\vv{\\text{u}} \\cdot \\vv{\\text{v}}&amp;=(3,2)\\cdot (-2,3) \\\\[1.5ex]&amp;=3\\cdot (-2) + 2 \\cdot 3 \\\\[1.5ex] &amp; = -6+6 \\\\[1.5ex] &amp; =\\bm{0} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u7ed3\u679c\u4e3a\u96f6\uff0c<strong>\u56e0\u6b64\u8fd9\u662f\u4e24\u4e2a\u5f7c\u6b64\u6b63\u4ea4\uff08\u6216\u5782\u76f4\uff09\u7684\u5411\u91cf<\/strong>\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-bfceefe77fc6ae5d21d70abf882f1d1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\bm{\\perp} \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u4e24\u4e2a\u5411\u91cf\u7528\u7b26\u53f7\u8868\u793a\u4e3a\u5782\u76f4<\/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-519f18355ad2b09638ea0d45fce173fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\perp}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u5782\u76f4\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u4e3a\u96f6\u3002\u7136\u800c\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u5411\u91cf\u79ef\uff08\u5411\u91cf\u4e4b\u95f4\u7684\u53e6\u4e00\u79cd\u4e58\u6cd5\uff09\u7ed9\u51fa\u76f8\u53cd\u7684\u7ed3\u679c\uff1a\u4e00\u4e2a\u5411\u91cf\u5782\u76f4\u4e8e\u53e6\u5916\u4e24\u4e2a\u5411\u91cf\u3002\u56e0\u6b64\uff0c\u4e86\u89e3\u5982\u4f55\u533a\u5206\u8fd9\u4e24\u79cd\u7c7b\u578b\u7684\u8fd0\u7b97\u975e\u5e38\u91cd\u8981\uff0c\u60a8\u53ef\u4ee5\u5728<a href=\"https:\/\/mathority.org\/cn\/\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u4ea4\u53c9\u516c\u5f0f\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u53c9\u79ef\u7684\u5c5e\u6027<\/a>\u4e2d\u770b\u5230\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-un-vector-perpendicular-u-ortogonal-a-otro\"><\/span>\u5982\u4f55\u8ba1\u7b97\u4e0e\u53e6\u4e00\u4e2a\u5411\u91cf\u5782\u76f4\u6216\u6b63\u4ea4\u7684\u5411\u91cf\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffe0aa\">\u8ba1\u7b97\u5e73\u9762\uff08\u5728 R2 \u4e2d\uff09\u4e2d\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u6700\u7b80\u5355\u65b9\u6cd5\u662f\u5c06\u5411\u91cf\u7684\u4e24\u4e2a\u5750\u6807\u4ea4\u9519\uff0c\u5e76\u5c06\u7b26\u53f7\u66f4\u6539\u4e3a 1\u3002<\/p>\n<p>\u4e3a\u4e86\u83b7\u5f97\u7a7a\u95f4\u4e2d\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u7684\u5411\u91cf\uff08\u5728 R3 \u4e2d\uff09\uff0c\u5fc5\u987b\u5c06\u4e24\u4e2a\u5750\u6807\u76f8\u4e92\u63d2\u5165\uff0c\u7136\u540e\u66f4\u6539\u5176\u4e2d\u4e00\u4e2a\u5750\u6807\u7684\u7b26\u53f7\uff0c\u6700\u540e\u5c06\u5750\u6807\u8bbe\u7f6e\u4e3a\u96f6\u3002<\/p>\n<p>\u8fd9\u6837\u60a8\u5c31\u53ef\u4ee5\u770b\u5230\u8ba1\u7b97\u4e00\u4e2a\u6b63\u4ea4\u5411\u91cf\u4e0e\u53e6\u4e00\u4e2a\u6b63\u4ea4\u5411\u91cf\u65f6\u7684\u5dee\u5f02\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u5b83\u4eec\u662f\u5426\u5177\u6709 2 \u4e2a\u6216 3 \u4e2a\u5750\u6807\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u6bcf\u79cd\u7c7b\u578b\u7684\u5411\u91cf\u6765\u89e3\u51b3\u4e00\u4e2a\u7ec3\u4e60\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-un-vector-perpendicular-u-ortogonal-en-el-plano-cartesiano\"><\/span>\u5728\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u627e\u5230\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u786e\u5b9a\u5782\u76f4\u4e8e\u4ee5\u4e0b\u4e8c\u7ef4\u5411\u91cf\u7684\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-e7317f02a44a1fe5e88995c6ab294552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u5b83\u662f\u4e00\u4e2a\u53ea\u6709\u4e24\u4e2a\u5206\u91cf\u7684\u5411\u91cf\uff0c\u4e3a\u4e86\u83b7\u5f97\u5782\u76f4\u5411\u91cf\uff0c\u9700\u8981\u4ea4\u66ff\u5176\u5206\u91cf\u5e76\u5bf9\u5176\u4e2d\u4e00\u4e2a\u5206\u91cf\u53d6\u53cd\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-318270e0576ad0c15e675699c6d746c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{=(-1,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u4ece\u70b9\u79ef\u516c\u5f0f\u9a8c\u8bc1\u8fd9\u4e9b\u786e\u5b9e\u662f\u5782\u76f4\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-1c66983a99e25383a527d0cfd895580f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\cdot \\vv{\\text{u}}=(4,1)\\cdot (-1,4) =0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" 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-7c19152b46f64fc00ffc1240af05ff4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-un-vector-perpendicular-u-ortogonal-en-el-espacio-cartesiano\"><\/span>\u786e\u5b9a\u7b1b\u5361\u5c14\u7a7a\u95f4\u4e2d\u7684\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u8ba1\u7b97\u4e0e\u4ee5\u4e0b\u4e09\u7ef4\u5411\u91cf\u6b63\u4ea4\u7684\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-afaddd121c95f2c502c2016e71a574eb_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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4e09\u5206\u91cf\u5411\u91cf\uff0c\u56e0\u6b64\u8981\u83b7\u5f97\u5782\u76f4\u5411\u91cf\uff0c\u6211\u4eec\u9700\u8981\u4ea4\u66ff\u5176\u4e24\u4e2a\u5206\u91cf\uff0c\u66f4\u6539\u5176\u4e2d\u4e00\u4e2a\u5206\u91cf\u7684\u7b26\u53f7\u5e76\u5c06\u5269\u4f59\u5750\u6807\u8f6c\u6362\u4e3a\u96f6\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-222eeaab5108a26f483c091087a2b725_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{u}}\\bm{=(3,-2,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u7528\u6807\u91cf\u79ef\u516c\u5f0f\u68c0\u67e5\u8fd9\u4e9b\u786e\u5b9e\u662f\u6b63\u4ea4\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-e76a1a210d6c5eae392104e71390efbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\cdot \\vv{\\text{u}}=(2,3,-1)\\cdot (3,-2,0) =0\" 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-7c19152b46f64fc00ffc1240af05ff4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-vectores-perpendiculares-y-ortogonales\"><\/span>\u5782\u76f4\u548c\u6b63\u4ea4\u5411\u91cf\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5782\u76f4\u5411\u91cf\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li><strong>\u5bf9\u79f0\u5173\u7cfb<\/strong>\uff1a\u5982\u679c\u4e00\u4e2a\u5411\u91cf\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5411\u91cf\uff0c\u5219\u8be5\u5411\u91cf\u4e5f\u5782\u76f4\u4e8e\u7b2c\u4e00\u4e2a\u5411\u91cf\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-aa3a2053276b703b1f53c493b25311ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\bm{\\perp}  \\vv{\\text{v}} \\ \\longrightarrow \\ \\vv{\\text{v}} \\bm{\\perp} \\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"116\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u65e0\u81ea\u53cd\u6027\u8d28<\/strong>\uff1a\u663e\u7136\uff0c\u6ca1\u6709\u5411\u91cf\u53ef\u4ee5\u5782\u76f4\u4e8e\u81ea\u8eab\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-153d5cde7f727d36c26bcca51f25980b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} \\ \\cancel{\\bm{\\perp}}} \\ \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5728\u6b27\u51e0\u91cc\u5f97\u51e0\u4f55\uff08R2 \u4e2d\uff09\u4e2d\uff0c\u5782\u76f4\u4e8e\u7b2c\u4e09\u4e2a\u5411\u91cf\u7684\u4efb\u4f55\u4e00\u5bf9\u5411\u91cf\u90fd\u5fc5\u987b\u5e73\u884c\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u4e00\u4e2a\u5411\u91cf\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5411\u91cf\uff0c\u5e76\u4e14\u8be5\u5411\u91cf\u4e5f\u5782\u76f4\u4e8e\u7b2c\u4e09\u4e2a\u5411\u91cf\uff0c\u5219\u7b2c\u4e00\u4e2a\u5411\u91cf\u548c\u6700\u540e\u4e00\u4e2a\u5411\u91cf\u662f\u5e73\u884c\u7684\u3002\u8fd9\u662f\u7531\u4e8e<a aria-label=\"undefined (abre en una nueva pesta\u00f1a)\" rel=\"noreferrer noopener\" href=\"https:\/\/es.wikipedia.org\/wiki\/Quinto_postulado_de_Euclides\" target=\"_blank\">\u6b27\u51e0\u91cc\u5f97\u7b2c\u4e94\u516c\u8bbe<\/a>\u3002<\/li>\n<\/ul>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u60a8\u8fd8\u5e94\u8be5\u77e5\u9053\uff0c\u7531\u4e8e\u8fd9\u4e9b\u7279\u6027\uff0c\u53ef\u4ee5\u4f7f\u7528\u5f00\u74f6\u5668\u89c4\u5219\u3002\u8fd9\u79cd\u6280\u672f\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u8ba1\u7b97\u4e00\u79cd\u5411\u91cf\u8fd0\u7b97\uff0c\u5982\u679c\u6ca1\u6709\u8fd9\u4e2a\u89c4\u5219\uff0c\u5c06\u9700\u8981\u5f88\u957f\u65f6\u95f4\u624d\u80fd\u89e3\u51b3\u3002\u60a8\u53ef\u4ee5\u901a\u8fc7\u5355\u51fb<a href=\"https:\/\/mathority.org\/cn\/\u53f3\u624b\u6cd5\u5219\u6216\u6cd5\u5219\/\">\u5f00\u74f6\u5668\u89c4\u5219<\/a>\u7684\u89e3\u91ca\u6765\u4e86\u89e3\u8fd9\u662f\u4ec0\u4e48\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"conceptos-relacionados-con-los-vectores-perpendiculares-u-ortogonales\"><\/span>\u4e0e\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf\u76f8\u5173\u7684\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u4e24\u79cd\u975e\u5e38\u63a5\u8fd1\u5782\u76f4\u5411\u91cf\u7684\u5411\u91cf\uff1a\u6cd5\u5411\u91cf\u548c\u6b63\u4ea4\u5411\u91cf\u3002\u5c3d\u7ba1\u5b83\u4eec\u5f7c\u6b64\u76f8\u5173\uff0c\u4f46\u6211\u4eec\u5e0c\u671b\u6f84\u6e05\u5b83\u4eec\u7684\u4e0d\u540c\u4e4b\u5904\uff0c\u4ee5\u907f\u514d\u4efb\u4f55\u53ef\u80fd\u7684\u6df7\u6dc6\u3002<\/p>\n<p><strong>\u6cd5\u5411\u91cf<\/strong>\u662f\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u5411\u91cf\u3002\u56e0\u6b64\uff0c\u5b83\u4e5f\u53ef\u4ee5\u5305\u542b\u5728\u77e2\u91cf\u6b63\u4ea4\u6027\u7684\u6982\u5ff5\u4e2d\uff0c\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5b83\u5782\u76f4\u4e8e\u5e73\u9762\u800c\u4e0d\u662f\u53e6\u4e00\u4e2a\u77e2\u91cf\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e24\u4e2a<strong>\u6b63\u4ea4\u5411\u91cf<\/strong>\u662f\u4e24\u4e2a\u76f8\u4e92\u6b63\u4ea4\u7684\u5411\u91cf\uff0c\u800c\u4e14\u662f\u5355\u4f4d\u5411\u91cf\uff08\u5927\u5c0f\u7b49\u4e8e 1\uff09\u3002<\/p>\n<p>\u6700\u540e\uff0c\u8fd8\u5e94\u8be5\u6ce8\u610f\u7684\u662f\uff0c\u4f7f\u7528<strong>\u6b63\u4ea4\u57fa<\/strong>\uff08\u7531\u5f7c\u6b64\u5782\u76f4\u7684\u5411\u91cf\u5f62\u6210\u7684\u5411\u91cf\u57fa\uff09\u751a\u81f3<strong>\u6b63\u4ea4\u57fa<\/strong>\u662f\u5f88\u5e38\u89c1\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u7b1b\u5361\u5c14\u53c2\u8003\u7cfb\u662f\u4e00\u4e2a\u6b63\u4ea4\u57fa\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5782\u76f4\uff08\u6216\u6b63\u4ea4\uff09\u5411\u91cf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u4eec\u662f\u4ec0\u4e48\uff0c\u5f53\u4e24\u4e2a\u5411\u91cf\u6b63\u4ea4\u65f6\uff0c\u5982\u4f55\u627e\u5230\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5411\u91cf\u7684 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%ad%a3%e4%ba%a4%e5%9e%82%e7%9b%b4%e5%90%91%e9%87%8f\/\"> <span class=\"screen-reader-text\">\u5782\u76f4\u6216\u6b63\u4ea4\u5411\u91cf<\/span> \u67e5\u770b\u5168\u6587 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