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Let a plane $P$ contain two lines $\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$, $\lambda \in \mathbb{R}$ and $\vec{r} = -\hat{j} + \mu(\hat{j} - \hat{k})$, $\mu \in \mathbb{R}$. If $Q(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from the point $M(1, 0, 1)$ to $P$, then $3(\alpha + \beta + \gamma)$ equals ______.
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