3. Consider the vector field given in Cartesian coordinates by A(r) = (r + y, 3x y, z). (a) Calculate V-A and VX A. Is A (i) incompressible? (ii) irrotational? (iii) conservative? (b) Evaluate the line integral = - S where C is the path y = x, z = 0, from the origin to the point (1, 1,0). (c) Evaluate the line integral J A dr, J = Jo A dr, where C is the path y = x, z = = 0, from the origin to the point (1,1,0). You should explicitly calculate the value of this integral. However, now explain why it would have been possible to write down this answer without doing the calculation. (d) Find the function o(x, y, z) such that A = Vo and o(0,0,0) = 0. Why can you be confident that such a function exists? (e) Show that your answers to parts (b) and (c) are consistent with your answer to part (d).