{"id":840,"date":"2010-01-01T10:39:36","date_gmt":"2010-01-01T02:39:36","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=840"},"modified":"2021-10-06T16:33:23","modified_gmt":"2021-10-06T08:33:23","slug":"%e5%90%91%e9%87%8f%e3%80%81%e5%96%ae%e4%bd%8d%e5%90%91%e9%87%8f-%ef%bc%88vector-unit-vector%ef%bc%89-%e5%9c%8b%e7%ab%8b%e5%bd%b0%e5%8c%96%e5%b8%ab%e7%af%84%e5%a4%a7%e5%ad%b8%e7%89%a9%e7%90%86","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%90%91%e9%87%8f%e3%80%81%e5%96%ae%e4%bd%8d%e5%90%91%e9%87%8f-%ef%bc%88vector-unit-vector%ef%bc%89-%e5%9c%8b%e7%ab%8b%e5%bd%b0%e5%8c%96%e5%b8%ab%e7%af%84%e5%a4%a7%e5%ad%b8%e7%89%a9%e7%90%86\/","title":{"rendered":"\u5411\u91cf\u3001\u55ae\u4f4d\u5411\u91cf \uff08Vector, Unit Vector\uff09"},"content":{"rendered":"

\u5411\u91cf\u3001\u55ae\u4f4d\u5411\u91cf\uff08Vector, Unit Vector\uff09
\n\u53f0\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a\u4e2d\u5b78\u908a\u923a\u7693\/\u53f0\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a\u4e2d\u5b78\u9ec3\u514b\u96c4\u8001\u5e2b\/\u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u5b78\u7cfb\u6d2a\u9023\u8f1d\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/span><\/p>\n

\u5728\u7269\u7406\u5b78\u4e0a\uff0c\u6211\u5011\u6709\u8a31\u8a31\u591a\u591a\u7684\u300c\u91cf\u300d\uff0c\u5c0d\u65bc\u90a3\u4e9b\u5728\u7d93\u904e\u5ea7\u6a19\u8f49\u63db\u5f8c\u4ecd\u7136\u80fd\u4fdd\u6301\u4e0d\u8b8a\u7684\u7269\u7406\u91cf\uff0c\u6211\u5011\u7a31\u4e4b\u70ba\u7d14\u91cf\uff0c\u7d14\u91cf\u662f\u4e0d\u5177\u6709\u65b9\u5411\u6027\u7684\u3002\u5c0d\u65bc\u90a3\u4e9b\u65e2\u6709\u5927\u5c0f\uff0c\u53c8\u5177\u6709\u65b9\u5411\u7684\u91cf\uff0c\u6211\u5011\u5c31\u7a31\u4e4b\u70ba\u300c\u5411\u91cf\u300d\u3002\u5728\u7269\u7406\u5b78\u4e0a\uff0c\u5f88\u591a\u7684\u300c\u91cf\u300d\u90fd\u662f\u5177\u6709\u65b9\u5411\u6027\u7684\uff0c\u50cf\u662f\uff1a\u4f4d\u79fb\u3001\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u3001\u529b\u77e9\u3001\u52d5\u91cf\u3001\u885d\u91cf\u7b49\u3002<\/p>\n

\"\"\u00a0\u4e00\u822c\u800c\u8a00\u6211\u5011\u662f\u4ee5\u7bad\u865f\u4f86\u8868\u793a\u5411\u91cf\uff0c\u5c0d\u65bc\u4e00\u500b\u7531A\u51fa\u767cB\u7d50\u675f\u7684\u5411\u91cf(\u5982\u5716)\uff0c\u6211\u5011\u8a18\u505a \\(\\vec {AB}\\)<\/p>\n

\u5c0d\u65bc\u67d0\u5411\u91cf \\(\\vec a\\) \u7684\u5927\u5c0f\uff0c\u6211\u5011\u8868\u793a\u6210 \\(|\\vec a|\\)<\/p>\n

\u7531\u65bc\u5411\u91cf\u50c5\u5177\u6709\u5927\u5c0f\u53ca\u65b9\u5411\uff0c\u56e0\u6b64\u7576\u5169\u500b\u5411\u91cf\u7684\u65b9\u5411\u3001\u5927\u5c0f\u90fd\u76f8\u7b49\u6642\uff0c\u6211\u5011\u5c31\u53ef\u4ee5\u8aaa\u9019\u5169\u500b\u5411\u91cf\u662f\u76f8\u7b49\u7684\u3002\u63db\u53e5\u8a71\u8aaa\u5411\u91cf\u5728\u7a7a\u9593\u4e2d\u662f\u53ef\u4ee5\u5e73\u79fb\u7684\uff0c\u5e73\u79fb\u5f8c\u7684\u5411\u91cf\u8207\u539f\u4f86\u7684\u5411\u91cf\u4ecd\u7136\u76f8\u7b49\u3002<\/p>\n

\u5c0d\u65bc\u6240\u6709\u7684\u5411\u91cf\uff0c\u6211\u5011\u90fd\u53ef\u4ee5\u7528\u55ae\u4f4d\u5411\u91cf\u4f86\u8868\u793a\u4ed6\u3002\u5728\u6578\u5b78\u4e0a\uff0c\u55ae\u4f4d\u5411\u91cf\u5c31\u662f\u9577\u5ea6\u70ba \\(1\\) \u7684\u5411\u91cf\u3002\u5728\u7a7a\u9593\u4e2d\uff0c\\(x,y,z\\) \u65b9\u5411\u4e0a\u7684\u55ae\u4f4d\u5411\u91cf\u5206\u5225\u70ba \\(\\hat i, \\hat j, \\hat k\\)<\/p>\n

\u4efb\u4f55\u4e00\u500b\u5411\u91cf\u90fd\u53ef\u4ee5\u7528\u4ed6\u5728 \\(x,y,z\\) \u8ef8\u4e0a\u7684\u5206\u91cf\u4f86\u8868\u793a\uff0c\u5373\uff1a\\(\\vec a = a_{x}\\hat i + a_{y}\\hat j + a_{z}\\hat k\\)
\n\u5c0d\u65bc\u67d0\u500b\u65b9\u5411\u4e0a\u7684\u55ae\u4f4d\u5411\u91cf\uff0c\u6211\u5011\u53ef\u4ee5\u4ee5 \\(\\displaystyle\\frac {\\vec a}{|\\vec a|}\\) \u4f86\u8868\u793a\u3002<\/p>\n

\u5411\u91cf\u7684\u52a0\u6e1b<\/span><\/h3>\n

\u5c0d\u65bc\u5411\u91cf\u6211\u5011\u4ecd\u7136\u53ef\u4ee5\u9032\u884c\u52a0\u6e1b\u3002\u6211\u5011\u5148\u628a\u8981\u8a08\u7b97\u7684\u5411\u91cf \\(\\vec{a},\\vec{b}\\) \u4ee5\u76f8\u540c\u7684\u6bd4\u4f8b\u5c3a\u5ea6\u7e6a\u51fa\uff0c\u4e26\u4f7f\u5169\u5411\u91cf\u5176\u4e2d\u4e00\u7aef\u982d\u5c3e\u76f8\u9023\uff0c\u5247\u53ef\u4ee5\u4f5c\u5716\u6cd5\u5c07\u53e6\u7aef\u982d\u5c3e\u9023\u7dda\u8868\u793a\u6b64\u5169\u5411\u91cf\u76f8\u52a0\u4e4b\u7d50\u679c(\u5c0d\u65bc\u591a\u500b\u5411\u91cf\u76f8\u52a0\u4ecd\u53ef\u5982\u6b64\u9032\u884c)\u3002
\n\"\"<\/a>\"\"<\/a>\"\"<\/a><\/p>\n

\u82e5\u8981\u8a08\u7b97\u5411\u91cf\u7684\u6e1b\u6cd5\uff1a\\(\\vec{a}-\\vec{b}\\)\uff0c\u5247\u5148\u5c07 \\(\\vec{b}\\) \u7684\u65b9\u5411\u53cd\u8f49\uff0c\u5f97\u5230 \\(-\\vec{b}\\)\u3002\u518d\u4ee5\u52a0\u6cd5\u7684\u65b9\u5f0f\u6c42\u51fa\u00a0\\(\\vec{a}+(-\\vec{b})\\)
\n\"\"<\/a>\"\"<\/a>
\n\u203b\u5411\u91cf\u7684\u52a0\u6e1b\u9075\u5b88\u4ea4\u63db\u7387\u548c\u7d50\u5408\u5f8b\uff1a<\/span><\/p>\n

\\(\\vec a + \\vec b = \\vec b + \\vec a \\)
\n\\(\\vec a + ( \\vec b + \\vec c ) = ( \\vec a + \\vec b ) + \\vec c\\)<\/p>\n

\u5411\u91cf\u7684\u4e58\u6cd5<\/span><\/h3>\n

\u5411\u91cf\u7684\u4e58\u6cd5\u53ef\u4ee5\u5206\u6210\u4e09\u985e\uff0c\u5411\u91cf\u548c\u7d14\u91cf\u7684\u4e58\u6cd5\u3001\u5411\u91cf\u7684\u5167\u7a4d\u3001\u5411\u91cf\u5916\u7a4d\u3002<\/p>\n

\u7576\u5411\u91cf\u8207\u7d14\u91cf\u76f8\u4e58\uff1a\\(|x|\\vec{a}\\)\uff0c\u4ed6\u6240\u4ee3\u8868\u7684\u610f\u7fa9\u662f \\(a\\) \u5411\u91cf\u7684\u65b9\u5411\u4e0d\u8b8a\uff0c\u91cf\u503c\u70ba \\(a\\) \u5411\u91cf\u539f\u672c\u7684\u91cf\u503c\u4e58\u4e0a \\(|x|\\)\u3002
\n\"\"<\/a>
\n\u5169\u500b\u5411\u91cf\u7684\u5167\u7a4d\u662f\u4e00\u7d14\u91cf\uff0c\u6211\u5011\u628a\u4ed6\u8a18\u505a \\(\\vec a \\cdot \\vec b\\)<\/p>\n

\u5176\u5b9a\u7fa9\u70ba \\(\\vec a \\cdot \\vec b = |\\vec a| |\\vec b| \\cos \\theta\\)<\/p>\n

\u5167\u7a4d\u6703\u6eff\u8db3\u5206\u914d\u5f8b\u3001\u4ea4\u63db\u5f8b\u3002\u5728\u7269\u7406\u5b78\u4e0a\uff0c\u529b\u4f5c\u529f\u7684\u554f\u984c\u7d93\u5e38\u6703\u7528\u5230\u5167\u7a4d\u4f86\u9032\u884c\u904b\u7b97\u3002<\/p>\n

\"\"<\/a>
\n\u5169\u500b\u5411\u91cf\u7684\u5916\u7a4d\u662f\u4e00\u5411\u91cf\uff0c\u8a18\u505a \\(\\vec a \\times \\vec b\\)\uff0c\u4ed6\u7684\u5927\u5c0f\u88ab\u5b9a\u7fa9\u70ba \\(\\vec a \\times \\vec b = |\\vec a| |\\vec b| \\sin \\theta\\)<\/p>\n

\\(\\theta\\) \u70ba \\(\\vec a, \\vec b\\) \u9593\u8f03\u5c0f\u7684\u593e\u89d2\uff0c\u65b9\u5411\u5247\u662f\u4ee5\u300c\u53f3\u624b\u5b9a\u5247\u300d\u4f86\u5224\u5b9a(\u5982\u5716)<\/p>\n

\"\"<\/a>
\n\u5916\u7a4d\u4e0d\u6eff\u8db3\u4ea4\u63db\u5f8b\u548c\u7d50\u5408\u5f8b\uff0c\u4f46\u537b\u6eff\u8db3\u5206\u914d\u5f8b\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u5411\u91cf\u3001\u55ae\u4f4d\u5411\u91cf\uff08Vector, Unit Vector\uff09 \u53f0\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a\u4e2d\u5b78\u908a\u923a\u7693\/\u53f0\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,107,3],"tags":[2233,2232,2234],"class_list":["post-840","post","type-post","status-publish","format-standard","hentry","category-physics01-02","category-physics00","category-physics01","tag-2233","tag-2232","tag-2234","loop-entry","cat-5","cat-107","cat-3","no-thumbnail"],"views":68510,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/840","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=840"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/840\/revisions"}],"predecessor-version":[{"id":90029,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/840\/revisions\/90029"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=840"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}