Question

State the condition under which a charged particle moving with velocity v goes undeflected in a magnetic field B

Answer 1

HeyMate
your answer is V || B

Answer 2

For the condition provided the velocity should be perpendicular to magnetic field.

The reason behind this is that the change in direction of velocity is because of change in its sine component, so if the value of sine component is zero ie $v*sin\alpha = 0$ where α is the angle between the velocity and field.

But since v≠0, sinα = 0 and for sinα to be 0, α = 0° or 180° and so for the given condition the velocity and direction of magnetic field must be parallel.