Question

Find the direction cosines of a line whose direction ratios are $2,-6,3$.

Answer 1

If the direction ratios are given as $x,y,z$, then the direction cosines are given by

$\frac{x}{\sqrt{x^2+y+z^2}},\frac{y}{\sqrt{x^2+y^2+z^2}},\frac{z}{\sqrt{x^2+y^2+z^2}}$

So, the direction cosines for direction ratios $2,-6,3$ are $\frac{2}{\sqrt{4+36+9}},\frac{-6}{\sqrt{4+36+9}},\frac{3}{\sqrt{4+36+9}}$

$=\pm \frac{2}{7},\mp \frac{6}{7},\pm \frac{3}{7}$