Vectors in Space · Medium problem

A drone's control software is deciding on a course: it adds the unit vector pointing toward beacon $A$ (bearing $\mathbf a = (4, 0, 3)$ from the drone) to the unit vector pointing toward beacon $B$ (bearing $\mathbf b = (0, 5, 12)$), and uses the result directly as its velocity vector in metres per second, splitting the difference between the two beacons. Starting at height $0$, find the drone's height after $1$ second of flight.