Q.
If $\overrightarrow{A}$ and $\overrightarrow{B}$ denote the sides of a parallelogram and its area is $\frac{1}{2}AB$($A\ $and $B$ are the magnitude of $\overrightarrow{A}$ and $\overrightarrow{B}$ respectively), the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is
A) 30${^\circ}$
B) 60${^\circ}$
C) 45${^\circ}$
D) 120${^\circ}$
Explanation
(a) Area of parallelogram $= |A \times B|$
$AB\ sin\theta = \frac{1}{2}AB$
$\therefore sin\theta = \frac{1}{2},\theta = 30{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.