Q. Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are inclined to each other at an angle $\theta$. Which of the following is the unit vector perpendicular to both $\overrightarrow{A}$ and $\overrightarrow{B}$?
A) $\frac{\overrightarrow{A} \times \overrightarrow{B}}{\overrightarrow{A} \bullet \overrightarrow{B}}$
B) $\frac{\widehat{A} \bullet \widehat{B}}{sin\theta}$
C) $\frac{\overrightarrow{A} \times \overrightarrow{B}}{ABsin\theta}$
D) $\frac{\widehat{A} \times \widehat{B}}{ABcos\theta}$
Explanation
(b) $\widehat{n} = \frac{\overrightarrow{A} \times \overrightarrow{B}}{ABsin\theta} = \frac{A\widehat{A} \times B\widehat{B}}{ABsin\theta} = \frac{\widehat{A} \times \widehat{B}}{sin\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.