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Question

If a,b and c are three non – coplanar vectors, then (a+b+c).((a+b)×(a+c)) equals

A
0
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B
[abc]
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C
2[abc]
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D
[abc]
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Solution

The correct option is D [abc]
We have,(a+b)×(a+c)=a×c+b×a+b×c
=a×b+b×cc×a(a+b+c).{(a+b)×(a+c)}
=(a+b+c).(a×b+b×cc×a)
=[aab]+[abc][aca][bab]+[bbc][bca][cab]+[cbc][cca]=[abc][bca][cab]=[abc]

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