JEE 2023 — Mathematics PYQ

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