a. Give an example of a vector field F (x, y, z) that has value 0 at only one point and such that curl F is nonzero everywhere. Be sure to identify the point and compute the curl.

b. Give an example of a vector field F (x, y, z) that has value 0 on precisely one line and such that curl F is nonzero everywhere. Be sure to identify the line and compute the curl.

c. Give an example of a vector field F (x, y, z) that has value 0 on a surface and such that curl F is nonzero everywhere. Be sure to identify the surface and compute the curl.