Two vectors $\vec{P}$ and $\vec{Q}$ are inclined to each other at angle $θ$ . Which of the following is the unit vector perpendicular to $\vec{P}$ and $\vec{Q}$ ?

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$\frac{\vec{P} \times \vec{Q}}{P \cdot Q}$

$\frac{\vec{P} \times \hat{Q}}{PQsin θ}$

$\frac{\hat{P} \times \hat{Q}}{\sin θ}$

$\frac{\hat{P} \times \vec{Q}}{PQcos θ}$

answer is B.

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Detailed Solution

$\hat{P} \times \hat{Q}, \vec{P} \times \hat{Q}$ as well as $\hat{P} \times \vec{Q}$ all are perpendicular to $\vec{P}$ and $\vec{Q}$ . Here only in case (2), the magnitude is equal to 1.

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