Final answer:
The value of w in the given velocity field, with components u = xy and v = xy³, cannot be determined without additional information about the system.
Step-by-step explanation:
The question provided involves calculating the components of a velocity field. The given components are u =xy and v = xy³. However, the question asks for the value of w, which typically would represent a third velocity component in a three-dimensional system. In many physical contexts, particularly involving velocity fields in fluid dynamics or electromagnetism, w may be expected to be zero if not explicitly defined, implying a two-dimensional flow or field. To determine the value of w precisely, however, you need additional information or assumptions about the system. For example, if it is known that the velocity field is strictly two-dimensional, then w may be assumed to be zero. Nonetheless, with the details provided, the value of w cannot be determined without additional context or information.