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If $\theta$ is the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$, then $\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a} \cdot \mathbf{b}|}$ equal to
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$\tan \theta$
Angle between the given vectors $\mathbf{a}$ and $\mathbf{b}$ is $\theta$. We know that, $\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a} \cdot \mathbf{b}|}=\frac{|\mathbf{a} \| \mathbf{b}| \sin \theta}{|\mathbf{a} \| \mathbf{b}| \cos \theta}=\tan \theta$.
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