It might be appreciated that you help me to figure out answers and steps too..

I don't know where to start with.. so please give me detailed steps.

Question 3 (20 marks) Let =x y+2xz' +zy' be a scalar field, (a) find Vo and div (Vo); (b) find the directional derivatives of $ at the point (1, 2, 0) in the direction of the vector (6 marks) a = 3i +4j -k; (10 marks) (c) calculate the magnitude of the maximum rate of change of o at the point (1, 2, 0) . (4 marks) Question 4 (20 marks) (a) Verify that the vector field F = yi + (x+zcosy)j +sin yk is irrotational, and find a scalar function f (x, y, z) for which F = Vf . (15 marks) (b) From the result in (a), evaluate / F . dr along any path from (0, 0, 0) to (3, 2, 0), where F =xi + yj + zk is the position vector of a moving particle. (5 marks) Question 5 (20 marks) Compute the following integrals using suitable method. (a) ff xy dx dy, where R is the region bounded by y=1, y=1+x, and y=3-x. R (10 marks) (b) SIT- V9-x?-y? ,dx dy dz , where V is the region bounded above by a sphere x?+ y? +z? =9 and bounded below by a plane z =1. (10 marks)