If the lines
\[
\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}
\]
and
\[
\frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7}
\]
are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).