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Find the shortest distance between the following two lines ${g}_{1}$ and ${g}_{2}:$

$\begin{aligned} {g}_{1} &: \frac{x-3}{2} = \frac{y+1}{-2} = z-2 \\ {g}_{2} &: x = \frac{y}{2} = -z+4. \end{aligned}$

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