{"id":9259,"date":"2024-06-13T08:01:01","date_gmt":"2024-06-13T00:01:01","guid":{"rendered":""},"modified":"2024-06-13T08:01:01","modified_gmt":"2024-06-13T00:01:01","slug":"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219","status":"publish","type":"post","link":"https:\/\/mushiming.com\/9259.html","title":{"rendered":"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219"},"content":{"rendered":"

\u5411\u91cf\u7684\u5185\u79ef\uff08\u70b9\u4e58\uff09<\/h2>\n

\u5b9a\u4e49<\/h3>\n

\u6982\u62ec\u5730\u8bf4\uff0c\u5411\u91cf\u7684\u5185\u79ef<\/strong>\uff08\u70b9\u4e58\/\u6570\u91cf\u79ef\uff09\u3002\u5bf9\u4e24\u4e2a\u5411\u91cf\u6267\u884c\u70b9\u4e58\u8fd0\u7b97\uff0c\u5c31\u662f\u5bf9\u8fd9\u4e24\u4e2a\u5411\u91cf\u5bf9\u5e94\u4f4d\u4e00\u4e00\u76f8\u4e58\u4e4b\u540e\u6c42\u548c\u7684\u64cd\u4f5c\uff0c\u5982\u4e0b\u6240\u793a\uff0c\u5bf9\u4e8e\u5411\u91cfa\u548c\u5411\u91cfb\uff1a<\/p>\n

\"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219\"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

a\u548cb\u7684\u70b9\u79ef\u516c\u5f0f\u4e3a\uff1a<\/p>\n

\"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

\u8fd9\u91cc\u8981\u6c42\u4e00\u7ef4\u5411\u91cfa\u548c\u5411\u91cfb\u7684\u884c\u5217\u6570\u76f8\u540c\u3002\u6ce8\u610f\uff1a\u70b9\u4e58\u7684\u7ed3\u679c\u662f\u4e00\u4e2a\u6807\u91cf(\u6570\u91cf\u800c\u4e0d\u662f\u5411\u91cf)<\/strong><\/p>\n

\u5b9a\u4e49<\/strong>\uff1a\u4e24\u4e2a\u5411\u91cfa<\/strong>\u4e0eb<\/strong>\u7684\u5185\u79ef\u4e3a a<\/strong>\u00b7b<\/strong> = |a<\/strong>||b<\/strong>|cos\u2220(a, b)\uff0c\u7279\u522b\u5730\uff0c0<\/strong>\u00b7a<\/strong> =a<\/strong>\u00b70<\/strong> = 0\uff1b\u82e5a<\/strong>\uff0cb<\/strong>\u662f\u975e\u96f6\u5411\u91cf\uff0c\u5219a<\/strong>\u4e0eb****\u6b63\u4ea4<\/strong>\u7684\u5145\u8981\u6761\u4ef6\u662fa<\/strong>\u00b7b<\/strong> = 0\u3002<\/p>\n

\u5411\u91cf\u5185\u79ef\u7684\u6027\u8d28\uff1a<\/h3>\n
    \n
  1. a<\/strong>^2 \u2265 0\uff1b\u5f53a<\/strong>^2 = 0\u65f6\uff0c\u5fc5\u6709a<\/strong> = 0. \uff08\u6b63\u5b9a\u6027\uff09<\/li>\n
  2. a<\/strong>\u00b7b<\/strong> = b<\/strong>\u00b7a<\/strong>. \uff08\u5bf9\u79f0\u6027\uff09<\/li>\n
  3. (\u03bba<\/strong> + \u03bcb<\/strong>)\u00b7c<\/strong> = \u03bba<\/strong>\u00b7c<\/strong> + \u03bcb<\/strong>\u00b7c<\/strong>\uff0c\u5bf9\u4efb\u610f\u5b9e\u6570\u03bb, \u03bc\u6210\u7acb. \uff08\u7ebf\u6027\uff09<\/li>\n
  4. cos\u2220(a<\/strong>,b<\/strong>) =a<\/strong>\u00b7b<\/strong>\/(|a<\/strong>||b<\/strong>|).<\/li>\n
  5. |a<\/strong>\u00b7b<\/strong>| \u2264 |a<\/strong>||b<\/strong>|\uff0c\u7b49\u53f7\u53ea\u5728a<\/strong>\u4e0eb<\/strong>\u5171\u7ebf\u65f6\u6210\u7acb.<\/li>\n<\/ol>\n

    \u5411\u91cf\u5185\u79ef\u7684\u51e0\u4f55\u610f\u4e49<\/h3>\n

    \u5185\u79ef\uff08\u70b9\u4e58\uff09\u7684\u51e0\u4f55\u610f\u4e49\u5305\u62ec\uff1a<\/p>\n

      \n
    1. \u8868\u5f81\u6216\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u5939\u89d2<\/li>\n
    2. b\u5411\u91cf\u5728a\u5411\u91cf\u65b9\u5411\u4e0a\u7684\u6295\u5f71<\/li>\n<\/ol>\n

      \u6709\u516c\u5f0f\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u63a8\u5bfc\u8fc7\u7a0b\u5982\u4e0b\uff0c\u9996\u5148\u770b\u4e00\u4e0b\u5411\u91cf\u7ec4\u6210\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u5b9a\u4e49\u5411\u91cfc<\/strong>\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u6839\u636e\u4e09\u89d2\u5f62\u4f59\u5f26\u5b9a\u7406\uff08\u8fd9\u91cca\u3001b\u3001c\u5747\u4e3a\u5411\u91cf\uff0c\u4e0b\u540c\uff09\u6709\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u6839\u636e\u5173\u7cfbc<\/strong>=a<\/strong>-b<\/strong>\u6709\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u5373\uff1a<\/p>\n

      a\u2219b=|a||b|cos\u2061(\u03b8)<\/p>\n

      \u5411\u91cfa\uff0cb\u7684\u957f\u5ea6\u90fd\u662f\u53ef\u4ee5\u8ba1\u7b97\u7684\u5df2\u77e5\u91cf\uff0c\u4ece\u800c\u6709a\u548cb\u95f4\u7684\u5939\u89d2\u03b8\uff1a<\/p>\n

      \u03b8=arccos\u2061(a\u2219b|a||b|)<\/p>\n

      \u8fdb\u800c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5224\u65ad\u4e24\u4e2a\u5411\u91cf\u662f\u5426\u540c\u4e00\u65b9\u5411\u6216\u6b63\u4ea4(\u5373\u5782\u76f4)\u7b49\u65b9\u5411\u5173\u7cfb\uff0c\u5177\u4f53\u5bf9\u5e94\u5173\u7cfb\u4e3a\uff1a<\/p>\n

      a\u2219b>0\u2192\u65b9\u5411\u57fa\u672c\u76f8\u540c\uff0c\u5939\u89d2\u57280\u00b0\u523090\u00b0\u4e4b\u95f4
      a\u2219b=0\u2192 \u6b63\u4ea4\uff0c\u76f8\u4e92\u5782\u76f4
      a\u2219b<0\u2192 \u65b9\u5411\u57fa\u672c\u76f8\u53cd\uff0c\u5939\u89d2\u572890\u00b0\u5230180\u00b0\u4e4b\u95f4<\/p>\n

      \u5411\u91cf\u7684\u5916\u79ef\uff08\u53c9\u4e58\uff09<\/h2>\n

      \u5b9a\u4e49<\/h3>\n

      \u6982\u62ec\u5730\u8bf4\uff0c\u4e24\u4e2a\u5411\u91cf\u7684\u5916\u79ef\uff0c\u53c8\u53eb\u53c9\u4e58\u3001\u53c9\u79ef\u5411\u91cf\u79ef\uff0c\u5176\u8fd0\u7b97\u7ed3\u679c\u662f\u4e00\u4e2a\u5411\u91cf<\/strong>\u800c\u4e0d\u662f\u4e00\u4e2a\u6807\u91cf\u3002\u5e76\u4e14\u4e24\u4e2a\u5411\u91cf\u7684\u5916\u79ef\u4e0e\u8fd9\u4e24\u4e2a\u5411\u91cf\u7ec4\u6210\u7684\u5750\u6807\u5e73\u9762\u5782\u76f4\u3002<\/p>\n

      \u5b9a\u4e49<\/strong>\uff1a\u5411\u91cfa<\/strong>\u4e0eb<\/strong>\u7684\u5916\u79efa<\/strong>\u00d7b<\/strong>\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u5176\u957f\u5ea6\u7b49\u4e8e|a<\/strong>\u00d7b<\/strong>| = |a<\/strong>||b<\/strong>|sin\u2220(a<\/strong>,b<\/strong>)\uff0c\u5176\u65b9\u5411\u6b63\u4ea4\u4e8ea<\/strong>\u4e0eb<\/strong>\u3002\u5e76\u4e14\uff0c(a<\/strong>,b<\/strong>,a<\/strong>\u00d7b<\/strong>)\u6784\u6210\u53f3\u624b\u7cfb\u3002
      \u7279\u522b\u5730\uff0c0<\/strong>\u00d7a<\/strong> = a<\/strong>\u00d70<\/strong> = 0<\/strong>.\u6b64\u5916\uff0c\u5bf9\u4efb\u610f\u5411\u91cfa<\/strong>\uff0ca<\/strong>\u00d7a<\/strong>=0<\/strong>\u3002<\/p>\n

      \u5bf9\u4e8e\u5411\u91cfa\u548c\u5411\u91cfb\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      a\u548cb\u7684\u5916\u79ef\u516c\u5f0f\u4e3a\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u5176\u4e2d\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u6839\u636ei\u3001j\u3001k\u95f4\u5173\u7cfb\uff0c\u6709\uff1a<\/p>\n

      \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

      \u5411\u91cf\u5916\u79ef\u7684\u6027\u8d28<\/h3>\n
        \n
      1. a<\/strong> \u00d7 b<\/strong> = -b<\/strong> \u00d7 a<\/strong>. \uff08\u53cd\u79f0\u6027\uff09<\/li>\n
      2. (\u03bba<\/strong> + \u03bcb<\/strong>) \u00d7 c<\/strong> = \u03bb(a<\/strong> \u00d7c<\/strong>) + \u03bc(b<\/strong> \u00d7c<\/strong>). \uff08\u7ebf\u6027\uff09<\/li>\n<\/ol>\n

        \u5411\u91cf\u5916\u79ef\u7684\u51e0\u4f55\u610f\u4e49<\/h3>\n

        \u5728\u4e09\u7ef4\u51e0\u4f55\u4e2d\uff0c\u5411\u91cfa\u548c\u5411\u91cfb\u7684\u5916\u79ef\u7ed3\u679c\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u6709\u4e2a\u66f4\u901a\u4fd7\u6613\u61c2\u7684\u53eb\u6cd5\u662f\u6cd5\u5411\u91cf<\/strong>\uff0c\u8be5\u5411\u91cf\u5782\u76f4\u4e8ea\u548cb\u5411\u91cf\u6784\u6210\u7684\u5e73\u9762\u3002<\/p>\n

        \u57283D\u56fe\u50cf\u5b66\u4e2d\uff0c\u5916\u79ef\u7684\u6982\u5ff5\u975e\u5e38\u6709\u7528\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u5411\u91cf\u7684\u5916\u79ef\uff0c\u751f\u6210\u7b2c\u4e09\u4e2a\u5782\u76f4\u4e8ea\uff0cb\u7684\u6cd5\u5411\u91cf\uff0c\u4ece\u800c\u6784\u5efaX\u3001Y\u3001Z\u5750\u6807\u7cfb\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n

        \"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219<\/p>\n

        \u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u5916\u79ef\u8fd8\u6709\u53e6\u5916\u4e00\u4e2a\u51e0\u4f55\u610f\u4e49\u5c31\u662f\uff1a|a<\/strong>\u00d7b<\/strong>|\u5728\u6570\u503c\u4e0a\u7b49\u4e8e\u7531\u5411\u91cfa\u548c\u5411\u91cfb\u6784\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u3002<\/p>\n

        Reference<\/h4>\n
          \n
        • http:\/\/blog.csdn.net\/dcrmg\/article\/details\/<\/li>\n
        • http:\/\/blog.csdn.net\/baimafujinji\/article\/details\/<\/li>\n
        • http:\/\/blog.csdn.net\/hunter_wwq\/article\/details\/<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"\u5411\u91cf\u7684\u5185\u79ef\u548c\u70b9\u79ef_\u5411\u91cf\u53c9\u4e58\u7684\u8fd0\u7b97\u6cd5\u5219\u5411\u91cf\u7684\u5185\u79ef\uff08\u70b9\u4e58\uff09\u5b9a\u4e49\u6982\u62ec\u5730\u8bf4\uff0c\u5411\u91cf\u7684\u5185\u79ef\uff08\u70b9\u4e58\/\u6570\u91cf\u79ef\uff09","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/9259"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=9259"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/9259\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=9259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=9259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=9259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}