Question 12. Recall that I = r sin($) cos(0), y = rsin($) sin(0), z = r cos($) using spherical coordinates. Let F be a vector field on R' given by F(x, y, z) = (sin(y + z) +2x)i+ (e"+= )j+ (x y)k (a) Determine the curl of F. (b) Let S be the unit sphere in Ro, that is, a sphere with radius 1 about the origin. Calculate the integral: V x F . n dA S (c) Let S be the unit sphere as in part (b). Calculate the integral: F . n dA S