Determine whether the following statements are true and give an explanation or counter example. a. any point on the z-axis has more than one representation in both cylindrical and spherical coordinates. b. the sets { (r, θ,z ): r = z } and {(rho,θ): =π/4} are the samea. the statement is true. in cylindrical coordinates, any point (x, y,z) = (0,0,z) on the z-axis is represented by (r,θ,z) = (0,θ,z), where theta is arbitrary. in spherical coordinates, the point (x, y,z) = (0,0,z) can be represented by (p, θ) = (z,0,θ) or (p, θ) = (-z, pi,θ) where theta is arbitrary. b. the statement is false. the origin (x, y,z) = (0,0,0) has only one unique representation in cylindrical coordinates. c. the statement is false. the origin (x, y,z) = (0,0,0) has only one unique representation in any coordinate system. d. the system is false. the origin (x, y,z) = (0,0,0) has only one unique representation in spherical coordinates.