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Question

If θ is the angle between any two vectors a and b , then a · b = a ×b when θ is equal to

(a) 0
(b) π/4
(c) π/2
(d) π

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Solution

(b) π/4

Let θ be the angle between aand b.We know a×b=a b sin θa. b=a b cos θa. b=a b cos θ=a' b cos θGiven: a. b=a×ba b cos θ=a b sin θcos θ=sin θθ=π4

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