Sample problem: Perpendicular magnetic and electric fields

A particle of charge q=1 $\mu C$ and mass m=10 g with initial velocity (v_x⁰,v_y⁰,v_z⁰)=(1,0,0) m/s enters a region of space in which there is a magnetic field given by $\vec{B}=(0,0,z)$ T and electric field $\vec{E}=(1,0,0)$ N/C. Find and plot the 3D trajectory this particle undergoes.