For each of of the three operations, grad (v), div (v) and curl (vx), answer the following questions (i) can the operation sensibly operated on a scalar function f(x, y, z) or a vector a vector function f(x, y, z), or none of them, or both of them. (ii) is the result a scalar or a vector? b) [10 pts] calculate the gradient of the following two scalar fields (i) fa(x, y, z) ecos() and (ii) fo(x, y, zcos (2y222) c) [10 pts the curl of the gradient of a scalar field f is always zero: we do not ask you to prove this rule in general for full credit, but check it for the two scalar fields fa and fo given in part b). d) [5 pts] calculate the divergence of f 2r2 sint+3r2+72 2 at the origin.