A particle is subjected to a force of constant magnitude that is...

Since the force is always perpendicular to the velocity, the power delivered by the force is zero ($\vec{F} \cdot \vec{v} = 0$).

Therefore, the work done by the force is zero, which implies that the kinetic energy and the speed $v$ of the particle remain constant.

The magnitude of the force is constant, so the magnitude of the acceleration $a = \dfrac{F}{m}$ is also constant.

Since the force is perpendicular to the velocity, the acceleration is purely centripetal and is given by $a = \dfrac{v^2}{R}$, where $R$ is the radius of curvature.

Because both $v$ and $a$ are constant, the radius of curvature $R$ is constant. Motion in a plane with a constant radius of curvature is a circular path.

Since the direction of motion changes continuously, the velocity and acceleration vectors are not constant.