Find the shortest distance and the vector equation of the line of shortest distance between the ...

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Find the shortest distance and the vector equation of the line of shortest distance between the lines given by:
\[
\begin{aligned}
\vec{r} & =(-\hat{i}+5 \hat{j})+\lambda(-\hat{i}+\hat{j}+\hat{k}) \\
-\text { and } \vec{r} & =(-\hat{i}-3 \hat{j}+2 \hat{k})+\mu(3 \hat{i}+2 \hat{j}+\hat{k})
\end{aligned}
\]
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