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If the distance between the plane, $23x - 10y - 2z + 48 = 0$ and the plane containing the lines $\frac{x + 1}{2} = \frac{y - 3}{4} = \frac{z + 1}{3}$ and $\frac{x + 3}{2} = \frac{y + 2}{6} = \frac{z - 1}{\lambda}$ $(\lambda \in \mathbb{R})$ is equal to $\frac{k}{\sqrt{633}}$, then $k$ is equal to ______.
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