Question

If u is a unit vector, prove that u · u = 1

Answer 1

by definition:
u · u = |u| |u|cosØ, where Ø is the angle between u and u
but that angle is 0° and |u| = 1

so u · u = |u| |u|cosØ = (1)(1)cos0 = (1)(1)(1) = 1