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Question

If a×(a×b)=b×(b×c) and (a.b)0, then [a b c]=

A
1
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B
2
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C
3
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D
0
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Solution

The correct option is D 0
Let solve LHS
^a×(a×b)=(a.b)a|a|2 b --(1)
RHS = b×(b×c)=(b.c)bb2c --(2)
Equating (1) & (2), we get
(a.b)a|a|2b=(bc)b|b|2c
As a,b and c are linearly dependent,
[a b c]=0

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