Q. The vectors $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}\$of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then, the magnitude of $\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}$ is
A) $3\sqrt{2}$
B) $2\sqrt{3}$
C) $2\sqrt{5}$
D) $5\sqrt{2}$
Explanation
(d)
$|\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}|^{2} = \left| \overrightarrow{\mathbf{a}}|^{2} + \left| \overrightarrow{\mathbf{b}}|^{2} - 2 \right|\overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|\cos{90{^\circ}}$
$25 + 25 - 2 \times 0 = 50$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}} \right| = 5\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.