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Question

If a+2b+3c=0, then b×c+c×a+a×b equals to:

A
6(b×c)
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B
(a×b)
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C
6(c×a)
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D
0
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Solution

The correct option is A 6(b×c)
a+2b+3c=0
(a+2b+3c)×c=0c×a=2(b×c)
(a+2b+3c)×b=0a×b=3(b×c)
b×c+c×a+a×b=(b×c)+2(b×c)+3(b×c)=6(b×c)=3(c×a)=2(a×b)

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