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 $\vec{OP}$?
Answer & explanation
Correct answer: option 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
$z = 2\sqrt{2} \cos 60^\circ$
$z = 2\sqrt{2} \times \frac{1}{2} = \sqrt{2}$
$(\sqrt{2}, 2, \sqrt{2})$