Mathematics Question from JEE Main 2023 · 11 April, Shift 1

Let a line $l$ pass through the origin and be perpendicular to the lines $l_1: \vec{r} = \left( \hat{i} - 11\hat{j} - 7\hat{k} \right) + \lambda \left( \hat{i} + 2\hat{j} + 3\hat{k} \right), \quad \lambda \in \mathbb{R}$ $l_2: \vec{r} = \left( -\hat{i} + \hat{k} \right) + \mu \left( 2\hat{i} + 2\hat{j} + \hat{k} \right), \quad \mu \in \mathbb{R}$ If $P$ is the point of intersection of $l$ and $l_1$, and $Q(\alpha, \beta, \gamma)$ is the foot of perpendicular from $P$ on $l_2$, then $9(\alpha + \beta + \gamma)$ is equal to: