JEE PHYSICS MCQ: MAGNETIC EFFECT OF CURRENT

There exists a uniform and constant magnetic field $B=1.67 T$ along positive $z$-axis. Simultaneously a proton and an alpha particle are projected from the origin with same speed $v=4 \sqrt{5} \times 10^5 \mathrm{~ms}^{-1}$ along positive and negative $x$-axis respectively. Find the separation between them when their velocities become mutually perpendicular for the first time. Ignore the force of interaction between them as well as any force other than magnetic force. Mass of the proton is $1.67 \times 10^{-27} \mathrm{~kg}$.