A particle of mass m and charge q is moving in a region where uniform, constant electric and mangetic fields `vec E and vec B` are present. `vec E and vec B` are parallel to each other. At time `t=0,` the velocity `vec v_0` of the particle is perpendicular to `vec E` (Assume that its speed is always `lt lt c`, the speed of light in vacuum). Find the velocity `vec v` of the particle at time `t`. You must express your answer in terms of `t, q, m,` the vector `vec v_0, vec E` and `vec B` and their magnitudes `vec v_0, vec E` and `vec B`.

Answer

`[(qt)/(m)vec(E)+vec(v)_(0)cos ((qBt)/(m))+(v_(0)(vec(v_(0))xxvec(B)))/(|v_(0)xxvec(B)|}sin ((qBt)/(m))]`