If a line has direction ratios $2, -1, -2$, determine its direction cosines.

$\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3}$

The correct answer is Option (2) → $\frac{2}{3}, -\frac{1}{3}, -\frac{2}{3}$ ##

We know that, if a line has direction ratios $a, b, c$, then Direction cosines of line are:

$\frac{a}{\sqrt{a^2 + b^2 + c^2}}, \frac{b}{\sqrt{a^2 + b^2 + c^2}}, \frac{c}{\sqrt{a^2 + b^2 + c^2}}$

Given direction ratios are: $2, -1, -2$

i.e., $a = 2, b = -1, c = -2$

$∴$ Direction cosines of the line are:

$\frac{2}{\sqrt{2^2 + (-1)^2 + (-2)^2}}, \frac{-1}{\sqrt{2^2 + (-1)^2 + (-2)^2}}, \frac{-2}{\sqrt{2^2 + (-1)^2 + (-2)^2}}$

Or, $\frac{2}{\sqrt{9}}, \frac{-1}{\sqrt{9}}, \frac{-2}{\sqrt{9}}$

Or, $\frac{2}{3}, \frac{-1}{3}, \frac{-2}{3}$