Let a plane P contain two lines r = i +λ( i + j ), λ ∈ R and r =- j +μ( j - k ), μ ∈ R. If Q (α, β, γ) is the foot of the perpendicular drawn from…

Let a plane P contain two lines $$\begin{aligned} & \overrightarrow{\mathrm{r}}=\hat{i}+\lambda(\hat{i}+\hat{j}), \lambda \in \mathbf{R} \text { and } \\ & \overrightarrow{\mathrm{r}}=-\hat{j}+\mu(\hat{j}-\hat{k}), \mu \in \mathbf{R} . \end{aligned} $$ If $\displaystyle \mathrm{Q}(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from the point $\displaystyle \mathrm{M}(1,0,1)$ to P , then $\displaystyle 3(\alpha+\beta+\gamma)$ equals \_\_\_\_.