) Let u and v be vectors in R 3 . (a) Express (u v) 2 + ku vk 2 in terms of kuk and kvk. (1 mark) (b) Suppose u = (a, b, c) and v = (d, e, f), where a, b, c, d, e, f are integers. Use Part (a) to show that the integer a 2 + b 2 + c 2 d 2 + e 2 + f 2 can be expressed as the sum of four squares. (2 marks) (c) Now let P = (a, b, c), Q = (d, e, f) R 3 be points on a sphere of radius 1 with centre O = (0, 0, 0) and let u = OP, v = OQ. Give a geometric interpretation of the point (u v, ku vk) in R