HMMT November 2015 U28

Find the shortest distance between the lines $\frac{x+2}{2}=\frac{y-1}{3}=\frac{z}{1}$ and $\frac{x-3}{-1}=\frac{y}{1}=\frac{z+1}{2}$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{5 \sqrt{3}}{3}

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