JEE Previous Year Question

Let $L_1\text{:}\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}$ and $L_2\text{:}\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}$ be two lines. Let $L_3$ be a line passing through
the point $\text{(}\alpha \text{,}\beta \text{,}\gamma \text{)}$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $L_1$, then $\text{|}5\alpha -11\beta -8\gamma \text{|}$ equals:

Topic: JEE PYQ

Answer: C. Full step-by-step solution below.