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Question

If a,b,c are non-coplanar non-zero vectors such that b×c=a, a×b=c, c×a=b, then

A
|a|=1
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B
|b|=1
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C
|a|+|b|+|c|=3
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D
None of these
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Solution

The correct options are
A |a|=1
B |b|=1
C |a|+|b|+|c|=3
We have b×c=a
[abc]=(a.a)=|a|2
Similarly [abc]=|b|2=|c|2
|a|=|b|=|c|=[abc]
Now , [b×cc×aa×b]=[abc]2

[abc]=[abc]2 (from the question)
But [abc]0.

So [abc]=1.

Hence, |a|=|b|=|c|=1.

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