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Consider the lines$$L_1:\frac{x+1}{3} = \frac{y+2}{1} = \frac{z+1}{2}$$$$L_1:\frac{x-2}{1} = \frac{y+2}{2} = \frac{z-3}{3}$$
The shortest distance between $$L_1$$ and $$L_2$$ is
0
$$\frac{17}{\sqrt{3}}$$
$$\frac{41}{5\sqrt{3}}$$
$$\frac{17}{5\sqrt{3}}$$
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