{"id":251,"date":"2023-07-10T10:33:39","date_gmt":"2023-07-10T10:33:39","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e5%b9%b3%e9%9d%a2\/"},"modified":"2023-07-10T10:33:39","modified_gmt":"2023-07-10T10:33:39","slug":"%e5%9e%82%e7%9b%b4%e5%b9%b3%e9%9d%a2","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e5%b9%b3%e9%9d%a2\/","title":{"rendered":"\u5782\u76f4\u5e73\u9762"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u4ec0\u4e48\u662f\u5782\u76f4\u5e73\u9762\uff0c\u5982\u4f55\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u662f\u5426\u5782\u76f4\uff0c\u5982\u4f55\u8ba1\u7b97\u5782\u76f4\u5e73\u9762\uff0c\u5782\u76f4\u5e73\u9762\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c&#8230; <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-planos-perpendiculares\"><\/span>\u4ec0\u4e48\u662f\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u4e24\u4e2a\u5e73\u9762\u4ee5\u76f4\u89d2 (90\u00b0) \u76f8\u4ea4\u65f6\u662f\u5782\u76f4\u7684\u3002<\/strong> <\/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\/plans-perpendiculaires-1.webp\" alt=\"\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\" class=\"wp-image-2938\" width=\"310\" height=\"325\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b64\u5916\uff0c\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u4e5f\u5f7c\u6b64\u6b63\u4ea4\u3002<\/p>\n<p>\u663e\u7136\uff0c\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u59cb\u7ec8\u4e3a\u96f6\uff0c\u56e0\u4e3a\u5b83\u4eec\u76f8\u4ea4\u4e8e\u4e00\u6761\u76f4\u7ebf\u3002\u867d\u7136\u770b\u8d77\u6765\u5f88\u7b80\u5355\uff0c\u4f46<a href=\"https:\/\/mathority.org\/cn\/\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\/\">\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u8ddd\u79bb<\/a>\u6982\u5ff5\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u6b64\u5982\u679c\u60a8\u5bf9\u6b64\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u8bbf\u95ee\u8be5\u94fe\u63a5\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5782\u76f4\u653e\u7f6e\u7684\u4e24\u4e2a\u5e73\u9762\u5e76\u4e0d\u662f\u5e73\u9762\u4e4b\u95f4\u552f\u4e00\u53ef\u80fd\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u56e0\u4e3a\u7a7a\u95f4\u4e2d\uff08\u5728 R3 \u4e2d\uff09\u7684\u4e24\u4e2a\u5e73\u9762\u4e5f\u53ef\u4ee5\u76f8\u4ea4\u3001\u5e73\u884c\u6216\u91cd\u5408\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-un-plano-es-perpendicular-a-otro\"><\/span>\u5982\u4f55\u77e5\u9053\u4e00\u4e2a\u5e73\u9762\u662f\u5426\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5e73\u9762\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u4e86\u5782\u76f4\u5e73\u9762\u7684\u5b9a\u4e49\u540e\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u77e5\u9053\u4e24\u4e2a\u5e73\u9762\u662f\u5426\u5782\u76f4\uff1a<\/p>\n<p><strong>\u5f53\u4e24\u4e2a\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u5782\u76f4\u65f6\uff0c\u5b83\u4eec\u5c31\u5782\u76f4\u3002\u56e0\u6b64\uff0c\u8981\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u662f\u5426\u76f8\u4e92\u5782\u76f4\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u5b83\u4eec\u7684\u6cd5\u5411\u91cf\u6240\u5f62\u6210\u7684\u89d2\u5ea6\uff0c\u5982\u679c\u5b83\u4eec\u5f62\u6210\u7684\u89d2\u5ea6\u4e3a 90\u00b0\uff0c\u5219\u8868\u793a\u4e24\u4e2a\u5e73\u9762\u662f\u5782\u76f4\u7684\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u627e\u5230\u4e24\u4e2a\u5e73\u9762\u7684\u5782\u76f4\u5ea6\uff0c\u60a8\u9700\u8981\u77e5\u9053<a href=\"https:\/\/mathority.org\/cn\/\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6<\/a>\u3002\u5982\u679c\u60a8\u4e0d\u8bb0\u5f97\u5982\u4f55\u64cd\u4f5c\uff0c\u53ef\u4ee5\u67e5\u9605\u94fe\u63a5\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u627e\u5230\u6211\u4eec\u7684\u89e3\u91ca\u4ee5\u53ca\u786e\u5b9a\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u7684\u5fc5\u8981\u516c\u5f0f\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002<\/p>\n<p>\u4f46\u7b80\u800c\u8a00\u4e4b\uff0c\u5f53\u4e24\u4e2a\u5411\u91cf\u7684\u70b9\u79ef\u4e3a\u96f6\u65f6\uff0c\u5b83\u4eec\u662f\u5782\u76f4\u7684\u3002\u56e0\u6b64\uff0c\u5f53\u4e24\u4e2a\u5e73\u9762\u76f8\u5173\u6cd5\u5411\u91cf\u7684\u70b9\u79ef\u4e3a 0 \u65f6\uff0c\u4e24\u4e2a\u5e73\u9762\u5c06\u662f\u5782\u76f4\u7684\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-dos-planos-perpendiculares\"><\/span>\u4e24\u4e2a\u5782\u76f4\u5e73\u9762\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f8b\u5982\uff0c\u8ba9\u6211\u4eec\u68c0\u67e5\u4ee5\u4e0b\u4e24\u4e2a\u5e73\u9762\u662f\u5426\u5782\u76f4\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-461f8b70561082ac05310f3bdbea280c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 3x-4y+2z+5 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ceed6a5e80f097883204588c20c06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 2x+5y+7z-6 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u5411\u91cf\u7684\u5750\u6807 X\u3001Y\u3001Z \u4e0e\u5176\u4e00\u822c\uff08\u6216\u9690\u5f0f\uff09\u65b9\u7a0b\u7684\u7cfb\u6570 A\u3001B\u3001C \u4e00\u81f4\u3002\u56e0\u6b64\uff0c\u6bcf\u4e2a\u5e73\u9762\u7684\u6cd5\u5411\u91cf\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-0767f496a5286c8e2ae26fb9d8fe209e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_1 =(3,-4,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-a0d0ceb987a550c197edc832e747928b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}_2 =(2,5,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u6cd5\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u6765\u68c0\u67e5\u5b83\u4eec\u662f\u5426\u662f\u4e24\u4e2a\u5782\u76f4\u5e73\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-94cfcef6a93720224eff0bd4891839ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{n}_1 \\cdot \\vv{n}_2 &amp; = (3,-4,2)\\cdot (2,5,7) \\\\[2ex] &amp; = 3 \\cdot 2 +(-4) \\cdot 5 +2 \\cdot 7 \\\\[2ex] &amp;=6-20+14 \\\\[2ex] &amp;\\bm{= 0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"236\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u6cd5\u5411\u91cf\u4e4b\u95f4\u7684\u70b9\u79ef\u4e3a 0\uff0c\u56e0\u6b64<strong>\u4e24\u4e2a\u5e73\u9762\u76f8\u4e92\u5782\u76f4<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-un-plano-perpendicular-a-una-recta-en-un-punto\"><\/span>\u8ba1\u7b97\u5782\u76f4\u4e8e\u76f4\u7ebf\u7684\u4e00\u70b9\u7684\u5e73\u9762<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5178\u578b\u7684\u5e73\u9762\u548c\u76f4\u7ebf\u95ee\u9898\u662f\u6c42\u5728\u7ed9\u5b9a\u70b9\u5904\u5782\u76f4\u4e8e\u76f4\u7ebf\u7684\u5e73\u9762\u7684\u65b9\u7a0b\u3002\u90a3\u4e48\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5b83\u662f\u5982\u4f55\u89e3\u51b3\u7684\uff1a<\/p>\n<ul>\n<li>\u6c42\u5782\u76f4\u4e8e\u76f4\u7ebf\u7684\u5e73\u9762\u7684\u65b9\u7a0b\u3002\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5173\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6afe6e8cf17f5596dfba598723950b26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u76f4\u622a\u4e86\u5f53\u5730\u8bf4\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-1ac7260ee9792daec4f32e1f200df01b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=3-2t \\\\[1.7ex] y=-1+4t \\\\[1.7ex] z=1+t \\end{cases} \\qquad \\qquad P(1,3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"314\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u5782\u76f4\u4e8e\u6240\u8ba8\u8bba\u7684\u5e73\u9762\u7684\u5411\u91cf\u3002\u548c\u559c\u6b22\u76f4\u7ebf<\/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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5782\u76f4\u4e8e\u5e73\u9762\uff0c\u5176\u6cd5\u5411\u91cf\u5c06\u4e0e\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u91cd\u5408\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8be5\u884c<\/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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u5176\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u5c31\u662f\u53c2\u6570\u524d\u9762\u7684\u9879<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" 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-b9328905f7ee6cbfcee10ac7c8b84149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(-2,4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5782\u76f4\u4e8e\u5e73\u9762\u7684\u5411\u91cf\u5c06\u4e0e\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u76f8\u540c\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-4e0ac55e7b5fae82ac79a70b71449d63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} =(-2,4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u8ba1\u5212\u7684\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u5982\u4e0b\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-373fe8f9bd73cd3280301259fb4f083e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi : \\ -2x+4y+1z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"213\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u786e\u5b9a\u7cfb\u6570 D \u7684\u503c\u5c31\u8db3\u591f\u4e86\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5176\u9648\u8ff0\u544a\u8bc9\u6211\u4eec\u5b83\u5c5e\u4e8e\u5e73\u9762\u7684\u70b9\u7684\u5750\u6807\u4ee3\u5165\u5176\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-cd7b14cad5f298f70a062fe512f9bd46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,3,-2)\" 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-2c8975f0cfb410904a9d7b5f0fefe73e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2\\cdot 1+4\\cdot 3-2+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"196\" style=\"vertical-align: -2px;\"><\/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-8fa3287f4f5dc0ae0c5deecb4b7c440e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2+12-2+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"161\" style=\"vertical-align: -2px;\"><\/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-27ba59475b36363e25411b5d5113ef7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -2px;\"><\/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-cdce1ad8fc5fc623a377d359ca9c1907_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=-8\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u5e73\u9762\u7684\u7b1b\u5361\u5c14\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-93487eba9a4a0a0e58417f13b45d8c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\pi : \\ -2x+4y+z-8=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"198\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u60a8\u60f3\u7ec3\u4e60\u66f4\u591a\u5173\u4e8e\u51e0\u4f55\u5bf9\u8c61\u4e4b\u95f4\u7684\u5782\u76f4\u5ea6\u7684\u7ec3\u4e60\uff0c\u60a8\u53ef\u4ee5\u8bbf\u95ee\u6211\u4eec\u7684\u5782\u76f4\u7ebf\u9875\u9762\u3002\u60a8\u5c06\u627e\u5230\u6709\u5173<a href=\"https:\/\/mathority.org\/cn\/\u5782\u76f4\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50-\u5782\u76f4\u5ea6\/\">\u5782\u76f4\u7ebf<\/a>\u6240\u9700\u4e86\u89e3\u7684\u6240\u6709\u4fe1\u606f\uff1a\u5f53\u4e24\u6761\u7ebf\u5782\u76f4\u65f6\u3001\u5982\u4f55\u8ba1\u7b97\u4e00\u6761\u7ebf\u4e0e\u53e6\u4e00\u6761\u7ebf\u7684\u5782\u76f4\u7ebf\u3001\u793a\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u7b49\u7b49\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-planos-perpendiculares\"><\/span>\u5782\u76f4\u5e73\u9762\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6240\u6709\u5782\u76f4\u5e73\u9762\u90fd\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li><strong>\u5bf9\u79f0\u5173\u7cfb<\/strong>\uff1a\u5982\u679c\u4e00\u4e2a\u5e73\u9762\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5e73\u9762\uff0c\u5219\u8be5\u5e73\u9762\u4e5f\u5782\u76f4\u4e8e\u7b2c\u4e00\u4e2a\u5e73\u9762\u3002\u5e73\u884c\u5e73\u9762\u4e5f\u5177\u6709\u8be5\u6027\u8d28\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-a65017e9c518a7647d5778548727798a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\bm{\\perp} \\pi_2 \\ \\longrightarrow \\ \\pi_2 \\bm{\\perp} \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"147\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u975e\u81ea\u53cd\u6027<\/strong>\uff1a\u663e\u7136\uff0c\u6ca1\u6709\u4e00\u4e2a\u5e73\u9762\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-59682cb1154e7a1d4206465c8fa28c72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 \\ \\cancel{\\bm{\\perp}}} \\ \\pi_1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u5b9a\u7406\uff1a<\/strong>\u5728\u4e09\u7ef4 (3D) \u7a7a\u95f4\u4e2d\uff0c\u5782\u76f4\u4e8e\u7b2c\u4e09\u5e73\u9762\u7684\u4efb\u4f55\u4e00\u5bf9\u5e73\u9762\u90fd\u5fc5\u987b\u5e73\u884c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u4e00\u4e2a\u5e73\u9762\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5e73\u9762\u5e76\u4e14\u8be5\u5e73\u9762\u4e5f\u5782\u76f4\u4e8e\u7b2c\u4e09\u5e73\u9762\uff0c\u5219\u7b2c\u4e00\u4e2a\u5e73\u9762\u548c\u6700\u540e\u4e00\u4e2a\u5e73\u9762\u5f7c\u6b64\u5e73\u884c\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u4ec0\u4e48\u662f\u5782\u76f4\u5e73\u9762\uff0c\u5982\u4f55\u786e\u5b9a\u4e24\u4e2a\u5e73\u9762\u662f\u5426\u5782\u76f4\uff0c\u5982\u4f55\u8ba1\u7b97\u5782\u76f4\u5e73\u9762\uff0c\u5782\u76f4\u5e73\u9762\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e5%b9%b3%e9%9d%a2\/\"> <span class=\"screen-reader-text\">\u5782\u76f4\u5e73\u9762<\/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":[15],"tags":[],"class_list":["post-251","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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