{"id":208,"date":"2023-07-11T22:02:35","date_gmt":"2023-07-11T22:02:35","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e5%87%8f%e6%b3%95-%e6%95%b0%e5%ad%97%e5%9b%be%e5%bd%a2-%e4%be%8b%e5%ad%90-%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0-%e5%87%8f%e6%b3%95\/"},"modified":"2023-07-11T22:02:35","modified_gmt":"2023-07-11T22:02:35","slug":"%e5%90%91%e9%87%8f%e5%87%8f%e6%b3%95-%e6%95%b0%e5%ad%97%e5%9b%be%e5%bd%a2-%e4%be%8b%e5%ad%90-%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0-%e5%87%8f%e6%b3%95","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e5%87%8f%e6%b3%95-%e6%95%b0%e5%ad%97%e5%9b%be%e5%bd%a2-%e4%be%8b%e5%ad%90-%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0-%e5%87%8f%e6%b3%95\/","title":{"rendered":"\u77e2\u91cf\u51cf\u6cd5"},"content":{"rendered":"

\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u4ee5\u56fe\u5f62\u65b9\u5f0f\u548c\u6570\u5b57\u65b9\u5f0f\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\u3002\u8981\u4ee5\u56fe\u5f62\u65b9\u5f0f\u51cf\u53bb\u5b83\u4eec\uff0c\u6709\u4e09\u79cd\u65b9\u6cd5\uff1a\u5e73\u884c\u56db\u8fb9\u5f62\u3001\u4e09\u89d2\u5f62\u548c\u591a\u8fb9\u5f62\u3002\u5728\u8fd9\u91cc\u60a8\u53ef\u4ee5\u533a\u5206\u6bcf\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u548c\u7f3a\u70b9\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u53d1\u73b0\u793a\u4f8b\u3001\u7ec3\u4e60\u548c\u9010\u6b65\u89e3\u51b3\u7684\u95ee\u9898\u3002 <\/p>\n

<\/span>\u5982\u4f55\u4ee5\u56fe\u5f62\u65b9\u5f0f\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\uff1f<\/span><\/h2>\n

\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5bf9\u5411\u91cf\u8fdb\u884c\u51e0\u4f55\u51cf\u6cd5\u3002\u663e\u7136\uff0c\u6240\u6709\u8fd9\u4e9b\u65b9\u6cd5\u90fd\u4f1a\u5f97\u5230\u76f8\u540c\u7684\u7ed3\u679c\uff0c\u4f46\u6211\u4eec\u5c06\u5411\u60a8\u89e3\u91ca\u6240\u6709\u65b9\u6cd5\uff0c\u4ee5\u4fbf\u60a8\u9009\u62e9\u60a8\u559c\u6b22\u7684\u65b9\u6cd5\u3002 \ud83d\udc4c<\/p>\n

\u8981\u4ec5\u51cf\u53bb 2 \u4e2a\u5411\u91cf\uff0c\u6709\u4e24\u79cd\u56fe\u5f62\u7a0b\u5e8f\uff1a\u5e73\u884c\u56db\u8fb9\u5f62\u6cd5<\/strong>\u548c\u4e09\u89d2\u5f62\u6cd5<\/strong>\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u8981\u89e3\u51b33\u4e2a\u6216\u66f4\u591a\u5411\u91cf\u7684\u51cf\u6cd5\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u591a\u8fb9\u5f62\u65b9\u6cd5<\/strong>\u3002<\/p>\n

\u56e0\u6b64\uff0c\u4e8b\u4e0d\u5b9c\u8fdf\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u4e86\u89e3\u6240\u6709\u8fd9\u4e9b\u65b9\u6cd5\u7684\u89e3\u91ca\u3002<\/p>\n

<\/span>\u5e73\u884c\u56db\u8fb9\u5f62\u65b9\u6cd5\u6216\u89c4\u5219<\/span><\/h3>\n

\u5e73\u884c\u56db\u8fb9\u5f62\u89c4\u5219<\/strong>\u6216\u5e73\u884c\u56db\u8fb9\u5f62\u65b9\u6cd5<\/strong>\u662f\u4e00\u79cd\u5141\u8bb8\u60a8\u901a\u8fc7\u5176\u56fe\u5f62\u8868\u793a\u4ee5\u975e\u5e38\u7b80\u5355\u7684\u65b9\u5f0f\u627e\u5230\u4e24\u4e2a\u5411\u91cf\u7684\u51cf\u6cd5\u7684\u8fc7\u7a0b\u3002\u5e94\u7528\u6b64\u6d41\u7a0b\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n

    \n
  1. \n
  2. \u9996\u5148\uff0c\u6211\u4eec\u5728\u56fe\u4e0a\u8868\u793a\u4e24\u4e2a\u5411\u91cf\uff0c\u5e76\u5c06\u5b83\u4eec\u653e\u7f6e\u5728\u540c\u4e00\u5e94\u7528\u70b9\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5c06\u4e24\u4e2a\u5411\u91cf\u7684\u539f\u70b9\u653e\u5728\u540c\u4e00\u70b9\u3002<\/span><\/li>\n
  3. \u5176\u6b21\uff0c\u6211\u4eec\u753b\u51fa\u8fd0\u7b97\u4e2d\u88ab\u51cf\u7684\u5411\u91cf\u7684\u76f8\u53cd\u5411\u91cf\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u53cd\u8f6c\u6b63\u5728\u51cf\u7684\u5411\u91cf\u3002<\/span><\/li>\n
  4. \u7136\u540e\u6211\u4eec\u5728\u76f8\u52a0\u5411\u91cf\u7684\u672b\u5c3e\u753b\u4e00\u6761\u4e0e\u7b26\u53f7\u6539\u53d8\u7684\u5411\u91cf\u5e73\u884c\u7684\u7ebf\u3002\u6211\u4eec\u7528\u53e6\u4e00\u4e2a\u5411\u91cf\u91cd\u590d\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u56fe\u5f62\uff08\u8be5\u89c4\u5219\u7684\u540d\u79f0\u7531\u6b64\u800c\u6765\uff09\u3002<\/span><\/li>\n
  5. \u6700\u540e\uff0c\u51cf\u6cd5\u7684\u7ed3\u679c\u5c06\u662f\u4ece\u4e24\u4e2a\u5411\u91cf\u7684\u5171\u540c\u539f\u70b9\u5230\u4e24\u6761\u5e73\u884c\u7ebf\u76f8\u4ea4\u70b9\u7684\u5411\u91cf\u3002<\/span><\/li>\n<\/ol>\n

    \u8003\u8651\u4ee5\u4e0b\u4e00\u822c\u793a\u4f8b\uff0c\u5176\u4e2d\u4f7f\u7528\u5e73\u884c\u56db\u8fb9\u5f62\u65b9\u6cd5\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\uff1a <\/p>\n

    \"\"<\/figure>\n

    <\/span>\u4e09\u89d2\u6cd5\u6216\u89c4\u5219<\/span><\/h3>\n

    \u4e09\u89d2\u5f62\u6cd5<\/strong>\u662f\u53e6\u4e00\u79cd\u53ef\u4ee5\u4ece\u56fe\u5f62\u4e2d\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\u7684\u8fc7\u7a0b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8981\u9075\u5faa\u7684\u6b65\u9aa4\u662f\uff1a<\/p>\n

      \n
    1. \n
    2. \u5c06\u4e24\u4e2a\u5411\u91cf\u653e\u5728\u540c\u4e00\u5e94\u7528\u70b9\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f7f\u4e24\u4e2a\u5411\u91cf\u5177\u6709\u76f8\u540c\u7684\u70b9\u4f5c\u4e3a\u5176\u539f\u70b9\u3002<\/span><\/li>\n
    3. \u5411\u91cf\u51cf\u6cd5\u7684\u7ed3\u679c\u662f\u4ece\u51cf\u6cd5\u5411\u91cf\u7684\u672b\u5c3e\u5230\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u672b\u5c3e\u7684\u7ebf\u6bb5\u3002\u5982\u679c\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u4e24\u4e2a\u5411\u91cf\u76f8\u51cf\uff0c\u5411\u91cf\u76f8\u51cf\uff0c\u5c31\u5f62\u6210\u4e86\u4e00\u4e2a\u4e09\u89d2\u5f62\u3002<\/span><\/li>\n<\/ol>\n

      \u8fd9\u662f\u4f7f\u7528\u4e09\u89d2\u5f62\u65b9\u6cd5\u8fdb\u884c\u5411\u91cf\u51cf\u6cd5\u7684\u793a\u4f8b\uff1a <\/p>\n

      \"\u5982\u4f55\u7528\u5934\u5c3e\u6cd5\u5bf9\u4e24\u4e2a\u5411\u91cf\u8fdb\u884c\u51cf\u6cd5\"<\/figure>\n

      \u8fd9\u79cd\u5411\u91cf\u51cf\u6cd5\u4e0e \u5411\u91cf\u52a0\u6cd5<\/a>\u7684\u5934\u5c3e\u6cd5<\/em>\u7c7b\u4f3c\u3002<\/p>\n

      <\/span>\u591a\u8fb9\u5f62\u6cd5<\/span><\/h3>\n

      \u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u5982\u4f55\u4ee5\u56fe\u5f62\u65b9\u5f0f\u89e3\u51b3\u4e24\u4e2a\u5411\u91cf\u7684\u51cf\u6cd5\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u5230\u5f53\u6211\u4eec\u6709\u4e24\u4e2a\u4ee5\u4e0a\u5411\u91cf\u65f6\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\u3002<\/p>\n

      \u5f53\u60a8\u60f3\u8981\u51cf\u53bb\u4e09\u4e2a\u6216\u66f4\u591a\u5411\u91cf\u65f6\uff0c\u6709\u4e00\u79cd\u6280\u672f\u53ef\u4ee5\u52a0\u5feb\u8ba1\u7b97\u901f\u5ea6\u5e76\u7acb\u5373\u51cf\u53bb\u6240\u6709\u5411\u91cf\u3002\u8be5\u6280\u672f\u79f0\u4e3a\u591a\u8fb9\u5f62\u65b9\u6cd5<\/strong>\uff0c\u7531\u8fde\u7eed\u5e94\u7528\u77e2\u91cf\u76f8\u52a0\u7684\u5934\u5c3e\u65b9\u6cd5\u7ec4\u6210\u3002<\/p>\n

      \u73b0\u5728\u60a8\u53ef\u80fd\u5728\u60f3\uff1a\u6dfb\u52a0<\/em>\u5411\u91cf\uff1f\u5b83\u88ab\u9519\u8bef\u5730\u7ea0\u6b63\u4e86……\u597d\u5427\uff0c\u4e0d\uff01\u5443\u5443<\/p>\n

      \u4e8b\u5b9e\u8bc1\u660e\uff0c\u4e24\u4e2a\u5411\u91cf\u76f8\u51cf\u4e0e\u4e00\u4e2a\u5411\u91cf\u52a0\u4e0a\u76f8\u51cf\u5411\u91cf\u7684\u76f8\u53cd\uff08\u6216\u8d1f\uff09\u5411\u91cf\u76f8\u540c\u3002\u8fd9\u662f\u7531\u4e8e\u5411\u91cf\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5\u6027\u8d28\uff1a<\/p>\n<\/p>\n

      \"\\vv{a}<\/p>\n<\/p>\n

      \u56e0\u6b64\uff0c\u7528\u591a\u8fb9\u5f62\u65b9\u6cd5\u51cf\u53bb3\u4e2a\u6216\u66f4\u591a\u5411\u91cf\u9700\u8981\u9075\u5faa\u7684\u6b65\u9aa4\u662f\uff1a<\/p>\n

        \n
      1. \n
      2. \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u6bcf\u4e2a\u51cf\u6cd5\u5411\u91cf\u7684\u9006\u5411\u91cf\u3002\u5f88\u7b80\u5355\uff0c\u5c31\u662f\u5c06\u6240\u6709\u76f8\u51cf\u7684\u5411\u91cf\u7684\u65b9\u5411\u548c\u65b9\u5411\u53cd\u8f6c\u5373\u53ef\u3002<\/span><\/li>\n
      3. \u7136\u540e\u6211\u4eec\u5c06\u6bcf\u4e2a\u76f8\u53cd\u7684\u5411\u91cf\u4e00\u4e2a\u63a5\u4e00\u4e2a\u5730\u653e\u7f6e\u5728\u60a8\u4e0d\u51cf\u53bb\u7684\u5411\u91cf\u65c1\u8fb9\u3002\u4f7f\u5f97\u4e00\u4e2a\u5411\u91cf\u7684\u539f\u70b9\u4e0e\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u7ec8\u70b9\u91cd\u5408\u3002<\/span><\/li>\n
      4. \u6700\u540e\uff0c\u5411\u91cf\u51cf\u6cd5\u7684\u7ed3\u679c\u662f\u5c06\u7b2c\u4e00\u4e2a\u5411\u91cf\u7684\u5f00\u5934\u4e0e\u6700\u540e\u4e00\u4e2a\u5411\u91cf\u7684\u7ed3\u5c3e\u8fde\u63a5\u8d77\u6765\u5f97\u5230\u7684\u5411\u91cf\u3002<\/span><\/li>\n<\/ol>\n

        \u770b\u4e0b\u9762\u7684\u793a\u4f8b\uff0c\u5176\u4e2d\u4f7f\u7528 4 \u4e2a\u5411\u91cf\u8fdb\u884c\u51cf\u6cd5\uff1a <\/p>\n

        \"\u7528\u591a\u8fb9\u5f62\u65b9\u6cd5\u8fdb\u884c\u5411\u91cf\u51cf\u6cd5\"<\/figure>\n

        \u8bf7\u6ce8\u610f\uff0c\u8981\u627e\u5230\u5411\u91cf\u7684\u76f8\u53cd\u5411\u91cf\uff0c\u8be5\u5411\u91cf\u7684\u4e24\u4e2a\u5206\u91cf\u5fc5\u987b\u6539\u53d8\u7b26\u53f7\u3002 <\/p>\n

        <\/span>\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u7684\u51cf\u6cd5\uff1f<\/span><\/h2>\n

        \u4e00\u65e6\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u5982\u4f55\u4ece\u56fe\u4e2d\u51cf\u53bb\u5411\u91cf\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u4ee5\u6570\u503c\u6216\u4ee3\u6570\u65b9\u5f0f\u8ba1\u7b97\u5411\u91cf\u51cf\u6cd5\u3002 <\/p>\n

        \n

        \u8981\u5bf9\u4e24\u4e2a\u5411\u91cf\u8fdb\u884c\u6570\u503c\u51cf\u6cd5\uff0c\u5fc5\u987b\u51cf\u53bb\u5b83\u4eec\u5404\u81ea\u7684\u5206\u91cf\u3002\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5c06\u4e24\u4e2a\u5411\u91cf\u7684 X \u5750\u6807\u76f8\u51cf\uff0c\u4e0e Y \u5750\u6807\u7c7b\u4f3c\u3002<\/p>\n<\/p>\n

        \"\\vv{\\text{u}}<\/p>\n<\/p>\n

        \"\\vv{\\text{u}}<\/p>\n<\/p>\n<\/div>\n

        \u4f8b\u5982\uff0c\u5411\u91cf\u4e4b\u95f4\u7684\u51cf\u6cd5<\/p>\n<\/p>\n

        \"\\vv{\\text{u}}<\/p>\n

        \u548c<\/p>\n

        \"\\vv{\\text{v}}=(2,<\/p>\n

        \u4e1c\u65b9\uff1a <\/p>\n<\/p>\n

        \"\\vv{\\text{u}}<\/p>\n<\/p>\n

        \"\\begin{aligned}<\/p>\n<\/p>\n

        <\/span>\u5df2\u89e3\u51b3\u7684\u5411\u91cf\u51cf\u6cd5\u95ee\u9898<\/span><\/h2>\n

        \u7ec3\u4e601<\/h3>\n

        \u4ee5\u56fe\u5f62\u65b9\u5f0f\u8ba1\u7b97\u5411\u91cf\u51cf\u6cd5<\/p>\n<\/p>\n

        \"\\vv{a}\"<\/p>\n

        \u8f83\u5c11\u7684<\/p>\n

        \"\\vv{b}:\"<\/p>\n<\/p>\n

        \"\u5411\u91cf\u51cf\u6cd5\u7684\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3\"<\/figure>\n
        \n
        \u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

        \u4e3a\u4e86\u5c06\u4e24\u4e2a\u5411\u91cf\u76f8\u51cf\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4e09\u89d2\u5f62\u65b9\u6cd5\u3002\u8fd9\u4e9b\u70b9\u5df2\u7ecf\u653e\u7f6e\u5728\u540c\u4e00\u5e94\u7528\u70b9\uff08\u5750\u6807\u539f\u70b9\uff09\uff0c\u56e0\u6b64\u51cf\u6cd5\u7684\u7ed3\u679c\u5c06\u662f\u4ece<\/p>\n<\/p>\n

        \"\\vv{b}\"<\/p>\n

        \u5728……\u7684\u6700\u540e<\/p>\n

        \"\\vv{a}.\"<\/p>\n<\/p>\n

        \"\u5411\u91cf\u51cf\u6cd5\u7684\u4f8b\u5b50\"<\/figure>\n
        <\/div>\n

        \u7ec3\u4e602<\/h3>\n

        \u4ee5\u56fe\u5f62\u65b9\u5f0f\u6c42\u5411\u91cf\u7684\u51cf\u6cd5<\/p>\n<\/p>\n

        \"\\vv{a}\"<\/p>\n

        \u8f83\u5c11\u7684<\/p>\n

        \"\\vv{b}:\"<\/p>\n<\/p>\n

        \"\u5411\u91cf\u51cf\u6cd5\u95ee\u9898\u5df2\u89e3\u51b3\"<\/figure>\n
        \n
        \u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

        \u4e3a\u4e86\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4e09\u89d2\u5f62\u6cd5\u5219\u3002\u8fd9\u4e9b\u70b9\u5df2\u7ecf\u653e\u7f6e\u5728\u540c\u4e00\u4e2a\u5e94\u7528\u70b9\uff08\u5728 X \u8f74\u548c Y \u8f74\u7684\u8d77\u70b9\uff09\uff0c\u56e0\u6b64\u51cf\u6cd5\u7684\u7ed3\u679c\u5c06\u662f\u4ece<\/p>\n<\/p>\n

        \"\\vv{b}\"<\/p>\n

        \u5728……\u7684\u6700\u540e<\/p>\n

        \"\\vv{a}.\"<\/p>\n<\/p>\n

        \"\u77e9\u9635\u51cf\u6cd5\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3\"<\/figure>\n
        <\/div>\n

        \u7ec3\u4e603<\/h3>\n

        \u4ee5\u56fe\u5f62\u65b9\u5f0f\u6c42\u89e3\u4ee5\u4e0b\u5411\u91cf\u8fd0\u7b97\uff1a <\/p>\n<\/p>\n

        \"\\vv{a}-\\vv{b}-\\vv{c}-\\vv{d}-\\vv{e}\"<\/p>\n<\/p>\n

        \"\u5982\u4f55\u51cf\u53bb\u4e24\u4e2a\u5411\u91cf\"<\/figure>\n
        \n
        \u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

        \u7531\u4e8e\u5411\u91cf\u6570\u91cf\u8d85\u8fc72\u4e2a\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u591a\u8fb9\u5f62\u6cd5\u5219\u6765\u89e3\u51b3\u5411\u91cf\u51cf\u6cd5\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f9d\u6b21\u8868\u793a\u5269\u4f59\u5411\u91cf\u7684\u76f8\u53cd\u5411\u91cf\u3002\u7ed3\u679c\u5c06\u662f\u4ece\u5411\u91cf\u539f\u70b9\u5f00\u59cb\u7684\u5411\u91cf<\/p>\n<\/p>\n

        \"\\vv{a}\"<\/p>\n

        \u5230\u6700\u540e\u4e00\u4e2a\u76f8\u53cd\u5411\u91cf\u7ed3\u675f\u7684\u5730\u65b9\u3002 <\/p>\n

        \"\u4ee5\u56fe\u5f62\u65b9\u5f0f\u5728\u4e24\u4e2a\u6216\u591a\u4e2a\u5411\u91cf\u4e4b\u95f4\u8fdb\u884c\u51cf\u6cd5\"<\/figure>\n
        <\/div>\n

        \u7ec3\u4e604<\/h3>\n

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        \"\\vv{a}=(-1,5)<\/p>\n<\/p>\n

        \"\\vv{a}-\\vv{b}\"<\/p>\n<\/p>\n

        \n
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        \"\\begin{aligned}<\/p>\n<\/p>\n

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        \u7ec3\u4e605<\/h3>\n

        \u89e3\u6790\u6c42\u89e3\u4ee5\u4e0b\u5411\u91cf\u8fd0\u7b97\uff1a <\/p>\n<\/p>\n

        \"\\vv{a}=(2,4)<\/p>\n<\/p>\n

        \"\\vv{a}-\\vv{b}<\/p>\n<\/p>\n

        \n
        \u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n

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        \"\\begin{aligned}<\/p>\n<\/p>\n

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