Question

Vector $\overrightarrow{P}=6\hat{i}+4\sqrt{2}\hat{j}+4\sqrt{2}\hat{k}$ makes angle from z-axis equal to:

• A. $co{s}^{-1}\left(\frac{\sqrt{2}}{5}\right)$
• B. $co{s}^{-1}\left(2\sqrt{2}\right)$
• C. $co{s}^{-1}\left(\frac{2\sqrt{2}}{5}\right)$
• D. None of these

Answer 1

The correct option is C $co{s}^{-1}\left(\frac{2\sqrt{2}}{5}\right)$

$\gamma =co{s}^{-1}\left(\frac{P_z}{P}\right)$
Here $P_z=4\sqrt{2}$
and $P=\sqrt{(6{)}^2+(4\sqrt{2}{)}^2+(4\sqrt{2}{)}^2}$
= 10
$\gamma =co{s}^{-1}\left(\frac{2\sqrt{2}}{5}\right)$