The direction ratios of two lines are given by a + b + c = 0, 2ab + 2ac– bc = 0. Then the angle between the lines is

$\begin{array}{l}\mathrm{a}+\mathrm{b}+\mathrm{c}=0\dots .\left(1\right)\Rightarrow a=-b-c\\ sub a in 2ab+2ac-bc=0\\ \Rightarrow (\mathrm{b}+2\mathrm{c})(2\mathrm{b}+\mathrm{c})=0\Rightarrow \mathrm{b}=-2\mathrm{c},\left(1\right)\Rightarrow \mathrm{a}=\mathrm{c}\\ \mathrm{a}:\mathrm{b}:\mathrm{c}=\mathrm{c}:-2\mathrm{c}:\mathrm{c}=(1,-2,1)\\ \Rightarrow \mathrm{c}=-2\mathrm{b}\Rightarrow \mathrm{a}=\mathrm{b}\\ \left(1\right)\Rightarrow \mathrm{a}:\mathrm{b}:\mathrm{c}=(\mathrm{b}:\mathrm{b}:-2\mathrm{b})=(1,1,-2)\\ \therefore \cos \mathrm{\theta }=\frac{|1-2-2|}{\sqrt{1+4+1}\sqrt{1+1+4}}=+\frac{1}{2}\Rightarrow \mathrm{\theta }=\frac{\mathrm{\pi }}{3}\end{array}$