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Question

If a,b,c are non coplanar non zero vectors such that b×c=a,a×b=c and c×a=b, then which of the following is not correct?

A
|a|=1
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B
a(b×c)=1
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C
|a||b||c|
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D
|a|+|b|+|c|=3
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Solution

The correct option is C |a||b||c|
b×c=aab×c=aa[abc]=|a|2
Similarly, we get
[abc]=|b|2[abc]=|c|2|a|2=|b|2=|c|2(1)

We know that
[b×c c×a a×b]=[abc]2[abc]=[abc]2[abc]=0,1

As |a|0, so
[abc]=1
Hence,
|a|=|b|=|c|=1

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