In a right handed coordinate system XY plane is horizontal and Z-axis is vertically npward. A uniform magnetic field exist in space in vertically npward direction with magnetic induction B. A particle with mass m and charge q is projected from the origin of the coordinate system at `t= 0` with a velocity vector given as
`vec(v) = v_(1) hat(i) + v_(2) hat(k)`
Find the velocity vector of the particle after time t.

Answer

`[(mv_(1))/(qB) sin ((qBt)/(m)), - (mv_(1))/(qB) (1 - cos ((qBt)/(m))), v_(2) t]`