Question

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

• A. $\frac{\overrightarrow{P}\times \overrightarrow{Q}}{PQ}$
• B. $\frac{\hat{P}\times \hat{Q}}{sin\theta }$
• C. $\frac{\hat{P}\times \hat{Q}}{PQsin\theta }$
• D. $\frac{\hat{P}\times \overrightarrow{Q}}{PQsin\theta }$

Answer 1

Answer: (B)

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

Unit vector perpendicular to $\overrightarrow{P}$ and $\overrightarrow{Q}$ will be given as $\frac{\overrightarrow{P}\times \overrightarrow{Q}}{|\overrightarrow{P}\times \overrightarrow{Q}|}$
= $\frac{\overrightarrow{P}\times \overrightarrow{Q}}{PQsin\theta }=\frac{\frac{\overrightarrow{P}}{P}\times \frac{\overrightarrow{Q}}{Q}}{sin\theta }=\frac{\hat{P}\times \hat{Q}}{sin\theta }$