Question

show that no line in the space can be make angle $\frac{\pi }{6}$ & $\frac{\pi }{4}$. With $x-$axis and $y-$axis.

Answer 1

Let $\theta +\alpha =\frac{\pi }{2}$

$\theta +\alpha =\frac{\pi }{6}+\frac{\pi }{4}$

$=\frac{2\pi }{12}+\frac{3\pi }{12}=\frac{5\pi }{12}\ne \frac{\pi }{2}$

No lines in space can make $\frac{\pi }{4}$ and $\frac{\pi }{6}$