IF the direction ratios of a line are proportional to 1, -3, 2 then its direction cosines are

$\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$

The direction ratios are proportional to 1, -3, 2.

So, direction cosines are

$\frac{1}{\sqrt{1^2+(-3)^2+2^2}}, \frac{-3}{\sqrt{1^2+(-3)^2+2^2}}, \frac{2}{\sqrt{1^2+(-3)^2+2^2}}  \, or \, \frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$