Consider the points A(3,4,12), B(7,−1,2) and C(0,6,9) in space. Let S be a sphere of radius 13 units with centre at the origin. Answer the following:
a. (i) Calculate the distance of each point A, B and C from the origin.
b. (ii) Using your results from part (i), determine for each point whether it lies inside S, on the surface of S, or outside S. Justify your answers.