(a) For the scalar field f(x, y) = xy, calculate the line integral of the function Vf from point O=(0,0) to point P = (xo, yo) along the paths C1, C2, and C3 as shown in the figure. Verify the fundamental theorem of gradients. (6) A G 0 (0,0) (b) Writing fV, verify whether Vis an irrotational vector or not. Can you make a comment on the integral fc V.dl where C=OAPBO, without doing the integral explicitly? (4)