Notes

v, E and B are Mutually Perpendicular…

v, E and B are Mutually Perpendicular – In this situation, if E and B are such that as shown in figure, then the particle will pass through the field with same velocity.
F = F_e + F_m = 0
i.e. a = (F/m) = 0
And in this situation, as |F_e| = |F_m|
i.e. qE = qvB ⇒ v = E/B