Let a and b be two non-zero vectors.
(i) State the greatest and least possible values of a⋅b in terms of ∣a∣ and ∣b∣.
(ii) Prove that the sign of a⋅b determines whether the angle between a and b is acute, right, or obtuse.
(iii) Give one numerical example of each of the three cases in part (ii) by choosing suitable 3-dimensional vectors, and verify your conclusion in each case.