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Question

For any three vectors a,b,c
a×(b+c)+b×(c+a)+c×(a+b) equals to

A
a+b+c
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B
[abc]
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C
a×b×c
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D
0
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Solution

The correct option is D 0
a×(a+c)+b×(c+a)+c×(a+b)
expanding by associated property [a×(b+c)=a×b+a×c]
[a×b+b×a]+[a×c+c×a]+[b×c+c×b]
[a×b=(b×a)]
[(a×b+b×a)=0]
0+0+0=0

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