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Question

If a,b,c are non-coplanar unit vectors such that a×(b×c)=b+c2, then the angle between a and b is
  1. π4
  2. π2
  3. π
  4. 3π4


Solution

The correct option is D 3π4
a×(b×c)=b+c2(a.c)b(a.b)c=b+c2[(a.c)12]b[(a.b)+12]c=0a.c=12,a.b=12
|a||c|cosθ=12,|a||b|cosϕ=12cosθ=12,cos=12θ=π4,ϕ=3π4.

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