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Question

[(a×b)×(b×c) (b×c)×(c×a) (c×a)×(a×b)][a×b b×c c×a] is equal to

A
|a|2|b|2|c|2
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B
[a b c]2
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C
[a×b b×c c×a]2
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D
|a|2 |b|2 |c|22
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Solution

The correct option is B [a b c]2
(a×b)×(b×c)=((a×b).c)b((a×b).b)c

=[abc]b

(b×c)×(c×a)=[abc]c

(c×a)×(a×b)=[abc]a

So, [[a b c]b [a b c]c [a b c]a][a b c]2

=[a b c]3×[b c a][a b c]2

=[a b c]2

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