Three Dimensional Geometry: JEE Main 2023 Mathematics question

Let a line $l$ pass through the origin and be perpendicular to the lines $l_{1}: \vec{r}=(\hat{\imath}-11 \hat{\jmath}-7 \hat{k})+\lambda(\hat{i}+2 \hat{\jmath}+3 \hat{k}), \lambda \in \mathbb{R}$ and $l_{2}: \vec{r}=(-\hat{\imath}+\hat{\mathrm{k}})+\mu(2 \hat{\imath}+2 \hat{\jmath}+\hat{\mathrm{k}}), \mu \in \mathbb{R}$. If $\mathrm{P}$ is the point of intersection of $l$ and $l_{1}$, and $\mathrm{Q}(\propto, \beta, \gamma)$ is the foot of perpendicular from P on $l_{2}$, then $9(\alpha+\beta+\gamma)$ is equal to _____________.