Question

If the direction cosines of line are $\frac{1}{c},\frac{1}{c},\frac{1}{c}$, then.

• A. $0<c<1$
• B. $c>2$
• C. $c>0$
• D. $c=\pm \sqrt{3}$

Answer 1

The correct option is D $c=\pm \sqrt{3}$

Given that the direction cosines of a line are $\frac{1}{c},\frac{1}{c},\frac{1}{c}$.

We know the sum of the squares of the direction cosines is one.

i.e. ${\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2=1$

$\Rightarrow \frac{3}{c^2}=1$

$\Rightarrow c^2=3$

$\Rightarrow c=\pm \sqrt{3}$