Problem 3. (max. 30 = 10+10+10 points) Consider the force field F(x, y) = (x2y2, x2y - (12 + ) + 1 )y) on R2, where A E R is a real parameter. (a) Show that there is no value of A for which F becomes conservative. (b) Find the work done by the force field on an object moving along the parametric curve a : [0, In(2)] - R2 with a(t) = (t, e-t). [Note. You are asked to find the work as a function of the parameter A.] (c) Can we find a value of A for which the work is minimised? If yes, determine this value, and the work done by the corresponding force field. Otherwise, explain why not