The angle between lines, whose direction cosines are given by $2l-m+2n=0$ and $lm+mn+nl=0$ is____

$$\begin{gathered} m=2l+2n \\ (l+n)(2l+2n)+nl=0 \\ 2l^2+2n^2+5nl=0 \\ 2{\left(\frac{l}{n}\right)}^2+5\left(\frac{l}{n}\right)+2=0 \\ (\frac{2l}{n}+1)(\frac{l}{n}+2)=0 \\ \frac{2l}{n}=-1\frac{l}{n}=-2 \\ 2l=-nl=-2n \end{gathered}$$

If  $2l=-n$
 $2l=-nl=\frac{-n}{2}=\frac{-m}{2}$
Dr’s  $\Rightarrow -1,2,2$
If  $l=-2n$
 $l=m=-2n$
Dr’s  $\Rightarrow 2,2,-1$
 $\cos \theta =0\Rightarrow \theta =\frac{\pi }{2}$