Q. If $\overrightarrow{\mathbf{x}}\$and $\overrightarrow{\mathbf{y}}$ are unit vectors and $\overrightarrow{\mathbf{x}} \bullet \overrightarrow{\mathbf{y}} = 0,$ then
A) $\left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right| = 1$
B) $\left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right| = \sqrt{3}$
C) $\left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right| = 2$
D) $\left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right| = \sqrt{2}$
Explanation
(d)
Given $\left| \overrightarrow{\mathbf{x}} \right| = \left| \overrightarrow{\mathbf{y}} \right| = 1$ and $\overrightarrow{\mathbf{x}} \bullet \overrightarrow{\mathbf{y}} = 0$
$\left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right|^{2} = \left| \overrightarrow{\mathbf{x}} \right|^{2} + |\overrightarrow{\mathbf{y}}|^{2} + 2(\overrightarrow{\mathbf{x}} \bullet \overrightarrow{\mathbf{y}})$
$\Longrightarrow \left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right|^{2} = 1 + 1 + 0$
$\Longrightarrow \left| \overrightarrow{\mathbf{x}} + \overrightarrow{\mathbf{y}} \right| = \sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.