Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let the direction cosines of the lines makes an angle $\alpha$ with each of coordinate axes. $\begin{array}{l}\therefore \ell +{\mathrm{m}}^2+{\mathrm{n}}^2=1\\ \therefore 3{\cos }^2\alpha =1\Rightarrow {\cos }^2\alpha =\frac{1}{3}\Rightarrow \cos \alpha =\pm \frac{1}{\sqrt{3}}\Rightarrow \ell =\mathrm{m}=\mathrm{n}=\frac{1}{\sqrt{3}}\end{array}$