3d Geometry

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 _____________.