Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being F(x, y, z): 1 (√x² + y² + z²)³ -x, -y, z). Show that the work done by the gravitational force as a particle moves from (x1, y₁, 2₁) to (x2, y2, 22) along any path depends only on the radii R₁ = √√√x² + y² + z² and R₂ = √√√x² + y² + z².

Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being F(x, y, z): 1 (√x² + y² + z²)³ -x, -y, z). Show that the work done by the gravitational force as a particle moves from (x1, y₁, 2₁) to (x2, y2, 22) along any path depends only on the radii R₁ = √√√x² + y² + z² and R₂ = √√√x² + y² + z².