Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

We know that ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$ and given $\alpha =\beta =\gamma$ $\therefore 3{\cos }^2\alpha =1\Rightarrow {\cos }^2\alpha =\frac{1}{3}\Rightarrow \cos \alpha =\cos \beta =\cos \gamma =\frac{1}{\sqrt{3}}$ Note: Angles are acute. So positive sign of $\frac{1}{\sqrt{3}}$ is considered.