Let a, b and c be three distinct points in a vector space V with an inner product. If $d(a,c) = d(a,b) + d(b,c)$ then $c-a = t(b-a)$ with $t \geq 1$.
I'm trying to show (without success so far) that the equality in the triangle inequality holds for the vectors (c-a) e (b-a), because, the equality holds if and only if (c-a) or (b-a) is a nonnegative multiple of the other.
Any tips?
Thank you very much.