We have,
$$
\begin{aligned}
& a+2 b+c=0 \\
& 11 b c+6 c a-14 a b=0
\end{aligned}
$$
From Eqs. (i) and (ii), we get
$$
\begin{aligned}
& 11\left(\frac{-a-c}{2}\right) c+6 a c-14 a\left(\frac{-a-c}{2}\right)=0 \\
\Rightarrow & -11 a c-11 c^2+12 a c+14 a^2+14 a c=0 \\
\Rightarrow & 14 a^2+15 a c-11 c^2=0 \\
\Rightarrow & 14 a^2+22 a c-7 a c-11 c^2=0 \\
\Rightarrow & (7 a+11 c)(2 a-c)=0 \\
\Rightarrow & a=\frac{-11}{7} c \text { and } a=\frac{c}{2}
\end{aligned}
$$
$\therefore$ Direction ratio of line are $(-11,2,7)$ and $(2,-3,4)$ Angle between lines are
$$
\begin{aligned}
& \therefore \cos \theta=-22-6+28=0 \\
& \because \quad \theta=\frac{\pi}{2}
\end{aligned}
$$