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I had a question in the final exam that asked what the angle between vectors a and b is if: $\vec a \cdot \vec b=|\vec a\times\vec b| $

Any hints please.

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    Oops. Actually, there should not be a determinant symbol.2012-06-28

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It is not hard to show that $\|u\times v\| = \|u\|\|v\| \sin(\theta),$ where $\theta\in[0,\pi]$ is the angle between $u$ and $v$. This should lead you right to a solution.

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    I do not think the cross product of two perpendicular vectors is $0$ ...2012-06-28