dot product of unit vectors

Hi

This is a bit of a basic question but i was just wondering out of curiosity.

Take i and j as unit vectors. What is i.i and j.j? The answer in both cases is 1. Is this because  you assumed the 2 vectors were on top of each other and so had an ange between then of 0 degrees so the dot product = |i|.|i| . cos(0) = 1

thanks