Question

If the direction ratios of a line are proportional to 1, −3, 2, then its direction cosines are
(a) $\frac{1}{\sqrt{14}},-\frac{3}{\sqrt{14}},\frac{2}{\sqrt{14}}$

(b) $\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}$

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

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

Answer 1

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


The direction ratios of the line are proportional to 1, $-$3, 2.

$\therefore$ The direction cosines of the line are

$$\begin{gathered} \frac{1}{\sqrt{1^2+{\left(-3\right)}^2+2^2}},\frac{-3}{\sqrt{1^2+{\left(-3\right)}^2+2^2}},\frac{2}{\sqrt{1^2+{\left(-3\right)}^2+2^2}} \\ =\frac{1}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{2}{\sqrt{14}} \end{gathered}$$