Let a line \( l \) pass through the origin and be perpendicular to the lines \( l_{1}:\ \vec{r}=(\hat{i}-11\hat{j}-7\hat{k})+\lambda(\hat{i}+2\hat{j}+3\hat{k}),\ \lambda\in\mathbb{R} \) and \( l_{2}:\ \vec{r}=(-\hat{i}+\hat{k})+\mu(2\hat{i}+2\hat{j}+\hat{k}),\ \mu\in\mathbb{R} \). 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 __________ .
