NIMCET 2017 — Mathematics PYQ

Concept:
The direction cosines of the vector are the corresponding coordinates of the vector divided by the length (magnitude) of the vector.

Calculation:

Here, $\vec{a}=(-2\hat{i}+\hat{j}-5\hat{k})$

$|\vec{a}|=\sqrt{(-2{)}^2+1^2+(-5{)}^2}=\sqrt{30}$

The direction cosines of the given vector are
$\frac{-2}{\sqrt{30}},\frac{1}{\sqrt{30}},\frac{-5}{\sqrt{30}}$

Hence, option (3) is correct.