若两个向量垂直，有什么定理和公式？ 两个向量垂直，有什么公式
\u82e5\u4e24\u4e2a\u5411\u91cf\u5782\u76f4\uff0c\u6709\u4ec0\u4e48\u5b9a\u7406\u548c\u516c\u5f0f\u4e24\u4e2a\u5411\u91cf\u76f8\u4e58\u7b49\u4e8e\u96f6
\u4e00\u3001\u4e24\u4e2a\u5411\u91cf\u5782\u76f4\uff0c\u6709\u5782\u76f4\u5b9a\u7406\uff1a
\u82e5\u8bbea=(x1,y1)\uff0cb=(x2,y2) \uff0ca\u22a5b\u7684\u5145\u8981\u6761\u4ef6\u662fa\u00b7b=0\uff0c\u5373(x1x2+y1y2)=0 \u3002
\u4e8c\u3001\u5411\u91cf\u5176\u4ed6\u5b9a\u7406
1\u3001\u5411\u91cf\u5171\u7ebf\u5b9a\u7406
\u82e5b\u22600\uff0c\u5219a//b\u7684\u5145\u8981\u6761\u4ef6\u662f\u5b58\u5728\u552f\u4e00\u5b9e\u6570\u03bb\uff0c\uff0c\u4f7f\uff0c\u82e5\u8bbea=(x1,y1)\uff0cb=(x2,y2) \uff0c\u5219\u6709
\uff0c\u4e0e\u5e73\u884c\u6982\u5ff5\u76f8\u540c\u3002\u5e73\u884c\u4e8e\u4efb\u4f55\u5411\u91cf\u3002
2\u3001\u5206\u89e3\u5b9a\u7406
\u5e73\u9762\u5411\u91cf\u5206\u89e3\u5b9a\u7406\uff1a
\u5982\u679c\u3001\u662f\u540c\u4e00\u5e73\u9762\u5185\u7684\u4e24\u4e2a\u4e0d\u5e73\u884c\u5411\u91cf\uff0c\u90a3\u4e48\u5bf9\u4e8e\u8fd9\u4e00\u5e73\u9762\u5185\u7684\u4efb\u4e00\u5411\u91cf\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u5bf9\u5b9e\u6570\uff0c\u4f7f\uff0c\u6211\u4eec\u628a\u4e0d\u5e73\u884c\u5411\u91cf\u3001\u53eb\u505a\u8fd9\u4e00\u5e73\u9762\u5185\u6240\u6709\u5411\u91cf\u7684\u57fa\u5e95\u3002
3\u3001\u4e09\u70b9\u5171\u7ebf\u5b9a\u7406
\u5df2\u77e5O\u662fAB\u6240\u5728\u76f4\u7ebf\u5916\u4e00\u70b9\uff0c\u82e5,\u4e14\u5219A\u3001B\u3001C\u4e09\u70b9\u5171\u7ebf\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5411\u91cf\u7684\u8fd0\u7b97\uff1a
\u8bbe\uff0c\u3002
1\u3001\u52a0\u6cd5
\u5411\u91cf\u52a0\u6cd5\u5411\u91cf\u7684\u52a0\u6cd5\u6ee1\u8db3\u5e73\u884c\u56db\u8fb9\u5f62\u6cd5\u5219\u548c\u4e09\u89d2\u5f62\u6cd5\u5219\uff0c\u3002
\u8bbea=(x1,y1)\uff0cb=(x2,y2)\uff0c\u5219a+b=(x1+x2,y1+y2)
\u5411\u91cf\u52a0\u6cd5\u7684\u8fd0\u7b97\u5f8b\uff1a
\u4ea4\u6362\u5f8b\uff1aa+b=b+a\uff1b
\u7ed3\u5408\u5f8b\uff1a(a+b)+c=a+(b+c)\u3002
2\u3001\u51cf\u6cd5
\u5982\u679ca\u3001b\u662f\u4e92\u4e3a\u76f8\u53cd\u7684\u5411\u91cf\uff0c\u90a3\u4e48a=-b\uff0cb=-a\uff0ca+b=0. 0\u7684\u53cd\u5411\u91cf\u4e3a0\uff0c
OA-OB=BA.\u5373\u201c\u5171\u540c\u8d77\u70b9\uff0c\u6307\u5411\u88ab\u5411\u91cf\u7684\u51cf\u6cd5\u51cf\u201d
a=(x1,y1)\uff0cb=(x2,y2) \uff0c\u5219a-b=(x1-x2,y1-y2).
c=a-b \u4ee5b\u7684\u7ed3\u675f\u4e3a\u8d77\u70b9\uff0ca\u7684\u7ed3\u675f\u4e3a\u7ec8\u70b9\u3002
\u52a0\u51cf\u53d8\u6362\u5f8b\uff1aa+(-b)=a-b
3\u3001\u6570\u4e58
\u5b9e\u6570\u03bb\u548c\u5411\u91cfa\u7684\u53c9\u4e58\u4e58\u79ef\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u8bb0\u4f5c\u03bba\uff0c\u4e14|\u03bba|=|\u03bb|*|a|\u3002
\u5f53\u03bb>0\u65f6\uff0c\u03bba\u7684\u65b9\u5411\u4e0ea\u7684\u65b9\u5411\u76f8\u540c\uff1b\u5f53\u03bb<0\u65f6\uff0c\u03bba\u7684\u65b9\u5411\u4e0ea\u7684\u65b9\u5411\u76f8\u53cd\uff1b\u5f53\u03bb=0\u65f6\uff0c\u03bba=0\uff0c\u65b9\u5411\u4efb\u610f\u3002\u5f53a=0\u65f6\uff0c\u5bf9\u4e8e\u4efb\u610f\u5b9e\u6570\u03bb\uff0c\u90fd\u6709\u03bba=0\u3002
4\u3001\u6570\u91cf\u79ef
\u82e5a\u3001b\u4e0d\u5171\u7ebf\uff0c\u5219\uff1b\u82e5a\u3001b\u5171\u7ebf\uff0c\u5219\u3002
\u5411\u91cf\u7684\u6570\u91cf\u79ef\u7684\u5750\u6807\u8868\u793a\uff1aa\u00b7b=x\u00b7x'+y\u00b7y'\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\uff1a\u5411\u91cf
如果向量a与向量b垂直 a（x1,y1）b(x2,y2)
则 a*b=x1×x2+y1×y2 （*为点乘）
数量积为〇
向量a*向量b=o，或者说它们的坐标之和等于0
相乘等于零
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