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 and passing through the point $(3, -4, 7)$.