NIMCET 2017 Question Paper with solutions

Concept:
The direction cosines of the vector is the corresponding coordinate of the vector divided by the length\/Magnitude of the vector. Calculation:
Here, $\overrightarrow{\mathit{a}}=\left(-2\stackrel{\wedge }{\mathit{i}}+\stackrel{\wedge }{\mathit{j}}-5\stackrel{\wedge }{\mathit{k}}\right)$
$\overrightarrow{\mid }\mathit{a}\mid =\sqrt{{\left(-2\right)}^2+1^2+{\left(-5\right)}^2}=\sqrt{30}$
The direction cosines of the given vector
$=\frac{-2}{\sqrt{30}},\frac{1}{\sqrt{30}},\frac{-5}{\sqrt{30}}$
Hence, option (4) is correct.