Final answer:
A vector changes if there is a change in its magnitude or direction. Velocity, as a vector, exemplifies this as it changes via acceleration when either speed or direction, or both, change. Therefore, the correct answer to the student's question is '4) any of these.'
Step-by-step explanation:
When discussing whether a vector changes, it is important to recognize that a vector is defined by both magnitude and direction. As such, a vector changes if any of these properties alter.
For instance, velocity is a vector, and it changes if there is a change in magnitude (or speed) or a change in direction. A car that turns a corner at the same speed is considered to be accelerating due to the change in direction of its velocity vector. Similarly, if a car speeds up or slows down, its velocity vector changes because its magnitude changes.
Therefore, the correct answer to the question 'A vector changes if:' is 4) any of these; meaning, a vector changes if its direction and magnitude both change, if its magnitude changes, or if its direction changes. The magnitude, units, and direction are all integral in defining a vector, differentiating vectors from scalars, which only have magnitude, but no direction.