Let the line of the shortest distance between the lines L_1: r =( i +2 j +3 k )+λ( i - j + k ) and L_2: r =(4 i +5 j +6 k )+μ( i + j - k ) intersect…

Let the line of the shortest distance between the lines $$\begin{aligned} & \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}) \text { and } \\ & \mathrm{L}_2: \overrightarrow{\mathrm{r}}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k}) \end{aligned} $$ intersect $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{L}_2$ at P and Q respectively. If $\displaystyle (\alpha, \beta, \gamma)$ is the mid point of the line segment PQ , then $\displaystyle 2(\alpha+\beta+\gamma)$ is equal to $\displaystyle \_\_\_\_$.