Answer:
Option A
Explanation:
We konow that angle berween two lines is
$\cos \theta=\frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}$
l+m+n=0
$\Rightarrow$ $l=-(m+n)$
$\Rightarrow$ $(m+n)^{2}=l^{2}$
$\Rightarrow$ $ m^{2}+n^{2}+2mn=m^{2}+n^{2}$
[ $\because l^{2}=m^{2}+n^{2},given$]
$\Rightarrow$ 2mn=0
when m=0 $\Rightarrow$ l=-n
Hence, (l,m,n) is (1,0,-1)
when n=0, then l=-m
Hence , (l,m,n) is (1,0,-1)
$\therefore$ $\cos\theta=\frac{1+0+0}{\sqrt{2}\times\sqrt{2}}$
= $\frac{1}{2}$
$\Rightarrow$ θ=$\frac{\pi}{3}$
