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W-ite the vector equations of the following lines and hence find is shortest distance between them:
\[
\frac{x+1}{2}=\frac{y+1}{-6}=\frac{z+1}{1} \text { and } \frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}
\]
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