Compute the curl of the vector field F = (3yz, 6xz, 8xy). curl(F(x, y, z)) = What is the curl at the point (-2, -4, 0)? curl(F (-2, -4, 0)) = Is this vector field irrotational or not? Choose\fFor each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 4(xy + 2) i+ 8(x2 + yz) 3 + 8(xz + y?) k. curl F = F (b) G = (8.xy + 2x3) i+ (4x2 + 2?) 3 + (2yz - 32) k. curl G = (c) H = (4xy + yz) i+ (2x2 + 2?) 3 + 3xz k. curl H = HLet F = 5(x + y) i + 5 sin(y) j. Find the line integral of F around the perimeter of the rectangle with corners (2, 0), (2, 2), (-3, 2), (-3, 0), traversed in that order. line integral =Use Green's Theorem to calculate the circulation of F = Sy + Alwyj around the unit circle, oriented counterclockwise. circulation = i, The divergence of a magnetic vector field B must be zero everywhere. Which of the following vector fields cannot be a magnetic vector field? (a) B(x, y, z) = (42 + 23)i+ (22 + y?)j - (22 + 2yz) k ? a magnetic vector field. (b) B(x, y, z) = -xi + yj - zk ? a magnetic vector field. (c) B(x, y, z) = (2xy - 22 + y )it (y-37)3 ? a magnetic vector field. (d) B(x, y, z) = (xy - xy)it (xy - x2y)j ? a magnetic vector field