Answer to Question #213879 in Linear Algebra for Hetisani Sewela

Question

Suppose u, v is the element of V and || u || = || v || = 1 with < u,v > = 1: Prove

that u = v.

Answer 1

It follows that $\cos \alpha=\frac{<u,v>}{||u||\cdot ||v||}=\frac{1}{1}=1,$ and hence $\alpha =0.$ Since the vectors $u$ and $v$ have the same direction and the same magnitude, we conclude that $u=v.$