If a charged particle moves unaccelerated through a region containing both electric and magnetic fields,which of the following must be true?

$A$ stream of charged particles enters a region with crossed electric and magnetic fields as shown in the figure below. On the other side is a screen with a hole that is right on the original path of the particles. Then,

$A$ collimated beam of charged and uncharged particles is directed towards a hole marked $P$ on a screen as shown below. If the electric and magnetic fields as indicated below are turned $ON$,which of the following statements is correct?

In the product $\overrightarrow{F} = q(\vec{v} \times \overrightarrow{B})$ where $\overrightarrow{B} = B \hat{i} + B \hat{j} + B_{0} \hat{k}$. Given $q = 1$,$\vec{v} = 2 \hat{i} + 4 \hat{j} + 6 \hat{k}$,and $\overrightarrow{F} = 4 \hat{i} - 20 \hat{j} + 12 \hat{k}$,what is the complete expression for $\overrightarrow{B}$?

$A$ proton moves with a velocity of $5 \times 10^6 \hat{j} \text{ ms}^{-1}$ through a uniform electric field $\vec{E} = 4 \times 10^6 [2 \hat{i} + 0.2 \hat{j} + 0.1 \hat{k}] \text{ Vm}^{-1}$ and a uniform magnetic field $\vec{B} = 0.2 [\hat{i} + 0.2 \hat{j} + \hat{k}] \text{ T}$. The approximate net force acting on the proton is

The electrostatic force $(\vec{F}_1)$ and magnetic force $(\vec{F}_2)$ acting on a charge $q$ moving with velocity $\vec{v}$ can be written as: