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.