Given is the line $g : \vec { X } = \left( \begin{array} { l } 1 \\ 7 \\ 2 \end{array} \right) + \lambda \cdot \left( \begin{array} { l } 3 \\ 4 \\ 0 \end{array} \right) , \lambda \in \mathbb { R }$, as well as another line $h$, which is parallel to $g$ and passes through the point $A ( 2 | 0 | 0 )$. The point $B$ lies on $g$ such that the lines AB and $h$ are perpendicular to each other.
Calculate the distance between $g$ and $h$.