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

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