Question
Assertion : If $\theta$ be the angle between $\vec{A}$ and $\vec{B}$, then
$
\tan \theta=\frac{\vec{A} \times \vec{B}}{\vec{A} \cdot \vec{B}}
$
Reason $\quad: \quad \vec{A} \times \vec{B}$ is perpendicular to $\vec{A} \cdot \vec{B}$

Answer

(d) $\frac{\vec{A} \times \vec{B}}{\vec{A} \cdot \vec{B}}=\frac{A B \sin \theta \hat{n}}{A B \cos \theta}=\tan \theta \hat{n}$where $\hat{n}$ is unit vector perpendicular to both $\vec{A}$ and $\vec{B}$.However $\frac{|\vec{A} \times \vec{B}|}{\vec{A} \cdot \vec{B}}=\tan \theta$

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