JEE Main 2014 (Online) 9th AprilQuestion 1
A line in the $3$-dimensional space makes an angle $\theta\ \left(0<\theta\le\frac\pi2\right)$ with both the $X$ and $Y$-axes. Then, the set of all values of $\theta$ is in the interval :
3D Geometry
Solution
$\cos^2\theta+\cos^2\theta+\cos^2\gamma=1$, so $2\cos^2\theta\le1$, i.e. $\cos\theta\le\frac1{\sqrt2}$, giving $\theta\in\left[\frac\pi4,\frac\pi2\right]$.