Question

Let the line of the shortest distance between the lines $L_1: \vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k})$and $L_2: \vec{r} = (4\hat{i} + 5\hat{j} + 6\hat{k}) + \mu(\hat{i} + \hat{j} - \hat{k})$ intersect $L_1$ and $L_2$ at $P$ and $Q$, respectively. If $(\alpha, \beta, \gamma)$ is the midpoint of the line segment $PQ$, then $2(\alpha + \beta + \gamma)$ is equal to \\_\\_\\_\\_.

Answer 1

The correct answer is