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Question

Define a×b and prove that a×b=(a.b)tanθ, where θ is the angle between a and b.

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Solution

a×b is defined as a c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.
L.H.S:|a×b|=|a||b|sinθ
R.H.S:(a.b)tanθ=|a||b|cosθtanθ=|a||b|sinθ=L.H.S
Hence proved.

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