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Question

Let a,b,c be three vectors having magnitudes 1,1 and 2 respectively. If a×(a×c)+b=0, then angle between a and c is

A
π6
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B
5π6
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C
π3
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D
Both A and B
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Solution

The correct option is C Both A and B
We know, aa×c
a×(a×c)=|a||a×c|^n
|a|=1,|a×c|=1×2cosθ=2cosθ (where θ is the angle between a and c)
We have, a×(a×c)+b=0
|2cosθ^n|=|b|cosθ=±12
θ=π/6,5π/6

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