作业帮请证明（a×b)·[（b×c)×（c×a)]=[a·(b×c)],a,b,c均为向量打错了，是=[a·（b×c)]^2
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/16 19:37:32
![请证明（a×b)·[（b×c)×（c×a)]=[a·(b×c)],a,b,c均为向量打错了，是=[a·（b×c)]^2](/uploads/image/z/2804406-6-6.jpg?t=%E8%AF%B7%E8%AF%81%E6%98%8E%EF%BC%88a%C3%97b%29%C2%B7%5B%EF%BC%88b%C3%97c%29%C3%97%EF%BC%88c%C3%97a%29%5D%3D%5Ba%C2%B7%28b%C3%97c%29%5D%2Ca%2Cb%2Cc%E5%9D%87%E4%B8%BA%E5%90%91%E9%87%8F%E6%89%93%E9%94%99%E4%BA%86%EF%BC%8C%E6%98%AF%3D%5Ba%C2%B7%EF%BC%88b%C3%97c%29%5D%5E2)
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请证明（a×b)·[（b×c)×（c×a)]=[a·(b×c)],a,b,c均为向量打错了，是=[a·（b×c)]^2
请证明（a×b)·[（b×c)×（c×a)]=[a·(b×c)],a,b,c均为向量
打错了，是=[a·（b×c)]^2
请证明（a×b)·[（b×c)×（c×a)]=[a·(b×c)],a,b,c均为向量打错了，是=[a·（b×c)]^2
公式1：(a ×b )×c =(a c )b -(b c )a
公式2：(a,b,c)=[a(b×c)]=(a×b）c=b(c×a).
公式3：c（c×a)=0
[（b×c)×（c×a)]=[b（c×a)]c-[c（c×a)]b=(a,b,c)c
（a×b)·[（b×c)×（c×a)]
=（a×b)·[(a,b,c)c]
=(a,b,c)[（a×b)c]
=(a,b,c)^2=[a(b×c)]^2