4. (a) For what values of a is F = (x + yz)i+a(y+2zx)] + (xy + z)k a conservative vector field? For this value of a, find a potential p such that F= Vip. (b) A particle is moved from the origin (0, 0, 0) to the point (1, 1, 1) along a straight-line path. Compute the work F dr, for the vector field in part (a), assuming an arbitrary value of a. For which values of a is your answer independent of the path taken?