Walker, Halliday & Resnick — Magnetic Fields: Problem 56

56 A proton moves through a uniform magnetic field given by $\vec{B} = (10\hat{i} - 20\hat{j} + 25\hat{k})\text{ mT}$. At time $t_1$, the proton has a velocity given by $\vec{v} = v_x\hat{i} + v_y\hat{j} + (2.0\text{ km/s})\hat{k}$ and the magnetic force on the proton is $\vec{F}_B = (4.0 \times 10^{-17}\text{ N})\hat{i} + (2.0 \times 10^{-17}\text{ N})\hat{j}$. At that instant, what are (a) $v_x$ and (b) $v_y$?