Let a line l pass through the origin and be perpendicular to the lines l_1: r =( i -11 j -7 k )+λ( i +2 j +3 k ), λ ∈ R and l_2: r =(- i + k )+μ(2 i…

Let a line $\displaystyle l$ pass through the origin and be perpendicular to the lines $$\begin{aligned} & l_1: \vec{r}=(\hat{\imath}-11 \hat{\jmath}-7 \hat{k})+\lambda(\hat{\imath}+2 \hat{\jmath}+3 \hat{k}), \lambda \in \mathbb{R} \text { and } \\ & l_2: \vec{r}=(-\hat{\imath}+\hat{k})+\mu(2 \hat{\imath}+2 \hat{\jmath}+\hat{k}), \mu \in \mathbb{R} . \end{aligned} $$ If P is the point of intersection of $\displaystyle l$ and $\displaystyle l_1$, and $\displaystyle \mathrm{Q}(\propto, \beta, \gamma)$ is the foot of perpendicular from $\displaystyle P$ on $\displaystyle l_2$, then $\displaystyle 9(\propto+\beta+\gamma)$ is equal to $\displaystyle \_\_\_\_$.