Question

If a line has the direction ratios $-18,12,-4$, then what are its direction cosines?

Answer 1

If a line has direction ratios of $-18,12$ and $-4$, then its direction cosines are
$\frac{-18}{\sqrt{{(-18)}^2+{\left(12\right)}^2+{(-4)}^2}},\frac{12}{\sqrt{{(-18)}^2+{\left(12\right)}^2+{(-4)}^2}},\frac{-4}{\sqrt{{(-4)}^2+{\left(12\right)}^2+{(-4)}^2}}$

i.e., $\frac{-18}{22},\frac{12}{22},\frac{-4}{22}\equiv \frac{9}{11},\frac{6}{11},\frac{-2}{11}$

Thus, the direction cosines are $-\frac{9}{11},\frac{6}{11}$ and $\frac{-2}{11}$.