Final answer:
In assessing the properties of vector fields, velocity is indeed a vector because it has both magnitude and direction, so a change would involve a vector. The direction of a vector can be described using components or magnitude and angle, and magnetic fields apply to the right-hand rule in currents.
Step-by-step explanation:
To address whether each vector field shown is a gradient, we must understand that a gradient field is derived from a scalar potential function. However, through the information provided, it seems appropriate to focus on the specific aspects of vector fields and their characteristics mentioned in the question. When discussing a change in velocity, it's important to clarify that velocity is indeed a vector, not a scalar, because it has both magnitude and direction. Therefore, the correct answer would be b. Yes, because velocity is a vector.
Regarding notation for describing the direction of vectors, one can use both component form (e.g., i, j, k notation) and magnitude-direction form (e.g., specifying magnitude and angle). For magnetic fields and the right-hand rule, if the magnetic field direction agrees with this rule as applied to a current, then we can affirmatively say it is consistent. Lastly, if a small needle is placed between two north poles of bar magnets, the needle can become magnetized by the surrounding magnetic field.