If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.

Question

$\begin{array}{1 1} k = \large\frac{-10}{7} \\ k = \large\frac{10}{7} \\ k = \large\frac{-7}{10} \\ k = \large\frac{7}{10}\end{array} $