Final answer:
The statement is true; the Biot-Savart law includes the Lorentz force law, which indicates that there is no force on a charged particle moving parallel to a magnetic field, making the Biot-Savart force law inapplicable in this situation.
Step-by-step explanation:
The statement that the Biot-Savart law does not apply if the velocity is parallel to the field direction is True. The Biot-Savart law deals with the magnetic field generated by a steady current and the force it exerts on a moving charge. According to the Lorentz force law, which is in part derived from the Biot-Savart law, the magnetic force on a charged particle is proportional to the cross product of the velocity of the particle and the magnetic field. This means that if the velocity of the particle is parallel to the magnetic field, the cross product is zero, and therefore there is no magnetic force on the particle. Charged particles with velocity parallel to the field will not experience a magnetic force and hence, will continue to move in a straight line along the field. This reinforces why the Biot-Savart force law is not applicable in such a scenario.