Two drones, $A$ and $B$, are performing a synchronized maneuver with constant velocity vectors. The velocity of drone $A$ is ${\mathbf{v}}_A=(15\mathbf{i}-25\mathbf{j}+10\mathbf{k}){m\; s}^{-1}$ and the velocity of drone $B$ is ${\mathbf{v}}_B=(k\mathbf{i}+10\mathbf{j}-4\mathbf{k}){m\; s}^{-1}$, where $k$ is a constant. Given that the direction of motion of drone $B$ is parallel to the direction of motion of drone $A$, determine the value of $k$.