Question

If a line has direction ratios $2,-1,-2$, then what are its direction cosines?

Answer 1

The direction cosines of a line are in the same ratio as that of the direction ratios, but the addition of their squares must yield $1$.

Thus, we find the direction cosines as under:

$\frac{2}{\sqrt{4+1+4}},\frac{-1}{\sqrt{4+1+4}},\frac{-2}{\sqrt{4+1+4}}$

It can be verified that $\frac{2^2+(-1{)}^2+(-2{)}^2}{4+1+4}=1$

Thus, the direction cosines are $\frac{2}{3},\frac{-1}{3},\frac{-2}{3}$