7. (a) (10 points) Show that the vector field F = sin y cos xi + cos y sin xj + z k is conser- vative, or equivalently satisfies the equations of the (curl) component test. (b) (10 points) Find a scalar potential function f(x, y, z) for the vector field F(x, y, z), and show all steps of your construction of f. . (c) (5 points) Evaluate the line integral F dr where C is a path from the point A(0, 1, 0) to B(,, 2).