Question

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

• A. $\frac{1}{3},-\frac{1}{3},-\frac{1}{3}$
• B. $3,-\frac{1}{3},-2$
• C. $\frac{2}{3},-\frac{1}{3},-\frac{2}{3}$
• D. $2,-\frac{1}{3},-\frac{2}{3}$

Answer 1

The correct option is C $\frac{2}{3},-\frac{1}{3},-\frac{2}{3}$

Let $a=2,b=-1$ and $c=-2$

Then the direction cosines of the line are

$\begin{array}{c}l=\frac{a}{\sqrt{a^2+b^2+c^2}}=\frac{2}{\sqrt{4+1+4}}=\frac{2}{3}\\ m=\frac{b}{\sqrt{a^2+b^2+c^2}}=\frac{-1}{\sqrt{4+1+4}}=\frac{-1}{3}\\ n=\frac{c}{\sqrt{a^2+b^2+c^2}}=\frac{-2}{\sqrt{4+1+4}}=\frac{-2}{3}\end{array}$