The velocity and acceleration vectors of a particle moving in a magnetic field are given by:

$\vec{v}=3 \hat{i}+4 \hat{j}$ and $\overrightarrow{a}=2 \hat{i}+\hat{j}$ respectively, Then:

(A) the magnetic field is along z-direction
(B) v = 3
(C) the kinetic energy of the particle is constant
(D) the acceleration is in x-z plane
(E) the particle is moving in x-y plane

Choose the correct answer from the options given below:

(A), (C), (E)

The correct answer is Option (4) → (A), (C), (E)

(A) Since, the velocity in the x-y direction, and if the particle's motion is affected by the magnetic force, the magnetic field lines must be in +z direction.

(C) Kinetic energy remains unchanged because the magnitude of velocity remains unchanged.

(E) The velocity vector ($\vec v$) lies in the x-y plane, and the accelration vector also lies in x-y plane. Hence, the motion is in x-y plane.