The points A(4,−2,5) and B(−6,8,−7) lie in space.
(i) A point C on AB satisfies the relation OC=21(OA+OB). Explain, without performing any calculation, the geometrical position of C on the line segment AB and justify your answer.
(ii) Verify the conclusion of part (i) by determining the ratio in which C divides AB internally.
(iii) Suppose instead that a point D on the same line satisfies OD=2OA−OB. Describe whether D divides AB internally or externally and support your reasoning.