If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$ then
If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$ then
$2 < \mathrm{c} < 3$
$\mathrm{c}=\pm 3$
$\mathrm{c}=\pm \sqrt{3}$
$\mathrm{c}=\pm \frac{1}{\sqrt{3}}$
Solution
Given $\ell=m=n=\frac{1}{c}$
We know that $\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \Rightarrow \frac{3}{\mathrm{c}^{2}}=1 \Rightarrow \mathrm{c}^{2}=3 \Rightarrow \mathrm{c}=\pm \sqrt{3}$