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Consider the three dimensional vector field (in the attached file) and the following three questions in the

Question

Consider the three dimensional vector field (in the attached file) and the following three questions in the

attached file. Please solve by 7:45PM PDT.

. Consider the three—dimensional vector field
F = (yz — 233312, axz — 232231 + 2, my + y)
where a, is a constant. (a) (2 points) There is exactly one value of a such that the vector field F is conservative. What is (1? Explain why f is conservative for
this value of a and no other. (b) (2 points) For the value of a found above, find a function f with
V f = F. Explain how you found f. (c) (2 points) Is there any value of a such that F is the curl of another
vector field? Explain.
Math