Question

Suppose u; v € V and ||u|| = ||v|| = 1 with < u; v > = 1: Prove that u = v

Answer 1

<u,v>=||u||$\cdot$ ||v||cos$\theta$

1=1$\cdot$1cos$\theta$

cos$\theta=1$

$\theta=0\degree$

So, the magnitudes of the vectors are equal, and the angle between them is 0$\degree$. That is the vectors are equal.