If f is a scalar field and f, g are vector fields, then f f, f · g, and f × g are defined by the following. (f f)(x, y, z) = f(x, y, z) f(x, y, z) (f · g)(x, y, z) = f(x, y, z) · g(x, y, z) (f × g)(x, y, z) = f(x, y, z) × g(x, y, z) find an identical expression, assuming that the appropriate partial derivatives exist and are continuous.