f a line in octant OXYZ makes equal angles with co-ordinate axes, then
f a line in octant OXYZ makes equal angles with co-ordinate axes, then
$l=m=n=\frac{1}{3}$
$l=m=n=-\frac{1}{3}$
$l=m=n=\frac{1}{\sqrt{3}}$
$l=m=n=-\frac{1}{\sqrt{3}}$
Solution
Let the direction cosines of the lines makes an angle $\alpha$ with each of coordinate axes.
$\begin{array}{l}
\therefore \quad \ell+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \\
\therefore \quad 3 \cos ^{2} \alpha=1 \Rightarrow \cos ^{2} \alpha=\frac{1}{3} \Rightarrow \cos \alpha=\pm \frac{1}{\sqrt{3}} \Rightarrow \ell=\mathrm{m}=\mathrm{n}=\frac{1}{\sqrt{3}}
\end{array}$