If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of $x$-axis and $y$-axis,…
If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of $x$-axis and $y$-axis, then the angle that the line makes with the positive direction of the $z-$axis is
$\frac{\pi}{6}$
$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
Solution
$\mathrm{l}=\cos \frac{\pi}{4}, m=\cos \frac{\pi}{4}$
we know $\mathrm{l}^2+\mathrm{m}^2+\mathrm{n}^2=1$
$\begin{aligned}
& \frac{1}{2}+\frac{1}{2}+n^2=1 \\
& \Rightarrow n=0
\end{aligned}$
Hence angle with positive direction of $\mathrm{z-}$ axis is $\frac{\pi}{2}$.