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Question

The vectors a×(b×c),b×(c×a) and c×(a×b) are

A
Collinear
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B
Coplanar
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C
Like vectors
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D
Linearly independent
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Solution

The correct option is C Coplanar
Solving
a×(b×c)=(ac)b(ab)c ________{1}
b×(c×a)=(ab)c(bc)a ________{2}
c×(a×b)=(cb)a(ca)b ________{3}
Add (1),(2) and (3), we get
a×(b×c)+b×(c×a)+c×(a×b)=0
So they are coplanar.

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