(a) State the coordinate formula for the point that divides internally a line segment joining A(x1,y1,z1) and B(x2,y2,z2) in the ratio m:n.
(b) Explain clearly why a sign change is required when the point divides the segment externally in the same ratio.
(c) For points A(x1,y1) and B(x2,y2) in the plane, write the general coordinates of the dividing point in both the internal and the external cases and comment on how the two sets of expressions differ.