Vector funtions 3- - 2 (0, 1) X (0, -1) 1) Determine if the given vector field is conservative or not, 2) determine the interpretation of the result and 3) verify that the solution of the problem satisfies all the conditions of Theorem 1. F(x, y, z) = xy z3i+ 2x2yz3j + 3x2y2z2k Theorem 1: yes F(x, y, z) is a field defined in all IRS whose component functions have continuous partial derivatives and rot F = 0, then F(x, y, z) is a conservative vector field. k d rot F = V x F = ax dz R OR rot F(x, y, z) = aQ Op OR Op az az ax. dx ay k