A line $\vec{OP}$ in space, represented by the figure below, has a magnitude of $2\sqrt{2}$ units.

Which of these are the direction ratios of $\vec{OP}$?

$(\sqrt{2}, 2, \sqrt{2})$

The correct answer is Option (2) → $(\sqrt{2}, 2, \sqrt{2})$ ##

The components of $\vec{OP}$ along the axes are found using trigonometry.

$x$-Component

$x = 2\sqrt{2} \cos 60^\circ$

$x = 2\sqrt{2} \times \frac{1}{2} = \sqrt{2}$

$y$-Component

$y = 2\sqrt{2} \cos 45^\circ$

$y = 2\sqrt{2} \times \frac{1}{\sqrt{2}} = 2$

$z$-Component

$z = 2\sqrt{2} \cos 60^\circ$

$z = 2\sqrt{2} \times \frac{1}{2} = \sqrt{2}$

$(\sqrt{2}, 2, \sqrt{2})$