1.27. a. In a coordinate system (x, y, z) where the z-axis is vertical, the gravitational force field at the surface of the earth can be written as F = (0,0, -gm), where g is the acceleration due to gravity and m is the mass of a falling object. (Note that g and m are both constant.) Show that D(x, y,z) = -gmz is a potential function for F, demonstrating that F is a conservative field. b. What is the work done by gravity in moving an object of mass m from the point (a, b, c) to (a, B, y)? Is this negative if c