Q. If $\overrightarrow{P} = 4\widehat{i} - 2\widehat{j} + 6\widehat{k}$ and $\overrightarrow{Q} = \widehat{i} - 2\widehat{j} - 3\widehat{k}$, then the angle which $\overrightarrow{P} + \overrightarrow{Q}$ makes with $x$-axis is
A) $\cos^{- 1}{\ \left( \frac{3}{\sqrt{50}} \right)}$
B) $\cos^{- 1}{\ \left( \frac{4}{\sqrt{50}} \right)}$
C) $\cos^{- 1}{\ \left( \frac{5}{\sqrt{50}} \right)}$
D) $\cos^{- 1}{\ \left( \frac{12}{\sqrt{50}} \right)}$
Explanation
(c) $\overrightarrow{P} + \overrightarrow{Q} = 5\widehat{i} - 4\widehat{j} + 3\widehat{k}$
cos $\ \alpha = \frac{5}{\sqrt{5^{2} + 4^{2} + 3^{2}}} = \frac{5}{\sqrt{50}}$
or $\alpha = \cos^{- 1}\left( \frac{5}{\sqrt{50}} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.