Explanation

(a) Lorentz force is the force exerted on a charged particle in a electromagnetic field. The particle will experience force due to electric field $qE$, and due to magnetic field (B) is $qv \times B$.
$F = qE + qv \times \mathbf{B} = qE + qv\ B\ sin\ \theta$
Where $\theta$ is angle between electric and magnetic field.
Since, the fields the parallel $\theta = 0.$
$\therefore F_{m} =$force due to magnetic field is zero.
Hence, only electric force ($F_{e} = qE)$ is exerted on the particle, so the particle move in a straight line with motion parallel to $B.$