Given: A charged particle is introduced at the origin \((x=0, y=0, z=0)\). initial velocity \(=\vec{v}\),
uniform electric field \(\vec{E}\).
uniform magnetic field \(\vec{B}\).
Also the values are given the table.
we need to find the cases where the particle will move in a straight line with constant velocity.
To move a particle with constant velocity;
Fnet \(=0\),
\(\Rightarrow\) The electric force \(=\) magnetic fore e.
\(\begin{gathered}
q E=q v B . \\
E=v B .
\end{gathered}\)
Now checking the options.
\(\begin{aligned}
&\text { A) (II) (iii) (s). } \\
&\text { (II) }=\vec{v}=\frac{E_0}{B_0} \hat{y} \text {. } \\
&\text { (iii) }=\vec{E}=-E_0 \hat{x} \\
&(s)=\vec{B}=B_0 \hat{Z} \text {. } \\
&-E_0 \hat{x}=E_0 \hat{B O} \hat{y}(B O \hat{z}) \\
\end{aligned}\)
\(\therefore\) (II) (iii) (s) is the correct option