Question

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

Answer 1

Given,direction ratios are -18,12,-4.

Here a=-18,b=12 and c=-4, then direction cosines of a line are

$(\frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}},\frac{c}{\sqrt{a^2+b^2+c^2}})=(\frac{-18}{\sqrt{(-{18}^2)+\left({12}^2\right)+(-4^2)}},\frac{12}{\sqrt{(-{18}^2)+\left({12}^2\right)+(-4^2)}}\frac{-4}{\sqrt{(-{18}^2)+\left({12}^2\right)+(-4^2)}})=(\frac{-18}{\sqrt{484}},\frac{12}{\sqrt{484}},\frac{-4}{\sqrt{484}})=(\frac{-18}{22},\frac{12}{22},\frac{-4}{22})=(-\frac{9}{11},\frac{6}{11},\frac{-2}{11})$

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