Thank you for reporting, we will resolve it shortly
Q.
If $m=1$ is the slope of a line $L$, then the product of the slopes of non-parallel lines which are inclined at an angle of $60^{\circ}$ with $L$ is
Let slope of line, which inclined with angle $60^{\circ}$ with line $L$ is $'n'$,
so $\tan 60^{\circ}=\left|\frac{n-1}{1+n}\right|=\sqrt{3}$
$\Rightarrow (n-1)^{2}=3(n+1)^{2}$
$\Rightarrow 2 n^{2}+8 n+2=0$,
which roots are slope of required lines so product of slopes $=1$