Determine whether the following pair of lines are parallel, intersecting or skew. Find the position vector of the intersection point (if any) and the angle between the lines.
\({{l}_{1}}\mathrm{:}x=y-1=z-6\), \({{l}_{2}}\mathrm{:}\frac{x-2}{3}=\frac{z-3}{2};y=2\)
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