Three point locations on the flat surface of a part have been measured by a CMM. The three point locations are (225.21, 150.23, 40.17), (14.24, 140.92, 38.29), and (12.56, 22.75, 38.02), where the units are mm. The coordinates have been corrected for probe radius.
(a) Determine the equation for the plane.
(b) To assess flatness of the surface, a fourth point is measured by the CMM. If its coordinates are (120.22, 75.34, 39.26), what is the vertical deviation of this point from the perfectly flat plane determined in (a)?