When a charged particle is projected with a certain velocity parallel to a magnetic field, it will continue its motion without any change. This is because the magnetic force acts perpendicular to both the velocity of the particle and the magnetic field. Since the velocity is parallel to the magnetic field, there is no component of velocity perpendicular to the magnetic field for the magnetic force to act on.
Option 1: A helical path is a curved 3D path, with both circular and linear components. However, in this case, the particle is projected parallel to the magnetic field, so there is no circular component to its motion. Therefore, it does not trace a helical path.
Option 2: A circular path is not traced because there is no perpendicular component of velocity for the magnetic force to act on.
Option 4: The charged particle does not come to rest instantly because there is no force to cause it to decelerate or stop.
In conclusion, option 3 is the correct answer because when a charged particle is projected parallel to a magnetic field, it will continue its motion without any change.