6. Curl & Divergence: a) Calculate the 2D curl in F: F = < 4x³y, xy²+x+> b) Find the 2D divergence for F in part a. c) Is F in part a source free? Irrotational? Explain why. d) Compute the divergence for F = < 15x, -6y, -6z>. State what this means. e) Find the divergence of the vector field F= < x²yz, -xy²z, -xyz²> f) Compute the curl for F= < 3xz³ey2, 2xz³ ey², 3xz² ey² >

Sketch the vector field of F (-y, 0) in the xy-plane. Be sure to draw enough vectors so that the pattern of the magnitude of the vectors and the direction of the vectors is clear. It is not required to label any points or vectors.

Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi).

Find the co-ordinate on the space curve given by the position vector r(t) 5 sin(2t)i +5 cos(2t)j + 24tk, which is at a distance of 267 units along the space curve from the co-ordinate (0,5,0).