VECTOR CALCULUS A vector field F in the xy-plane is said to have ideal flow if the divergence of F is O and the curl of F is 0 on a simply connected region. Let (a) F(x, y) = (x-3x)i+ (y-3xy)j. Show that div F-0 and curl F-0, thus F has ideal flow. (b) Find a potential function (x, y). (c) If F(x, y) = f(x, y)i+g(x, y)j and div F = 0, then there exists a function (x, y), called a stream function, such that f(x, y) =, and g(x, y). Find the stream function for the field given by F(x, y) = (x-3x)i + (y-3xy)j (d) Show that the potential function (x, y) and the stream function (x, y) satisfy Laplace's equation P+P = x + y = 0.