If the dc’s of two lines are given by l + m + n =0, mn -2ln + lm = 0 then the angle
between the lines is

$$\begin{gathered} \mathrm{If} \mathrm{the} \mathrm{dcs}(\mathrm{l},\mathrm{m},\mathrm{n}) \mathrm{of} \mathrm{two} \mathrm{lines} \mathrm{are} \mathrm{connected} \mathrm{by} \mathrm{the} \mathrm{relations} \\ al+bm+cn=0\text{ and }fmn+gnl+hlm=0\text{, } \\ \mathrm{then} \mathrm{the} \mathrm{lines} \mathrm{are} \text{ perpendicular if }\frac{\mathrm{f}}{\mathrm{a}}+\frac{g}{b}+\frac{h}{c}=0 \end{gathered}$$

Comparing given relations l + m + n =0, mn -2ln + lm = 0 

a=1,b=1,c=1,f=1g=-2,h=1

$\frac{\mathrm{f}}{\mathrm{a}}+\frac{\mathrm{g}}{\mathrm{b}}+\frac{\mathrm{h}}{\mathrm{c}}=\frac{1}{1}-\frac{2}{1}+\frac{1}{1}=0\Rightarrow \mathrm{Angle} \mathrm{between} \mathrm{the} \mathrm{lines}=\frac{\mathrm{\pi }}{2}$