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Question

If a and b are two non-zero non-collinear vectors such that a×b=1 and a . b=3, then the angle between a and b is _____________.

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Solution

For nonzero non collinear vectors a and bGiven a×b=1 a·b=3Since by lagrange's identity,a×b2+a.b2=a2 b2i.e. 1+3=a2 b2i.e. 4=a2 b2i.e. a b=2a.b=abcosθ where θ is angle between a and b3=2cosθi.e. cosθ=32i.e. θ=π6

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