Unit vectors in $\Bbb R^n$ Suppose that $x$ and $y$ are unit vectors in $\Bbb R^n$. Show that if $\left\Vert{{x+y}\over2}\right\Vert=1$ , then $x =y$.
Please enlighten me for this problem!
Thanks in advance!

$$1=1^2=||\frac{x+y}{2}||^2=\frac{1}{4}<(x+y),(x+y)>$$
$$4=<x,x>+2<x,y>+<y,y>=2+2<x,y>$$
$$<x,y>=1$$ So x and y are the same unit vector. Otherwise $|<x,y>|<1$ or $<x,y>=-1$ if $y=-x$.
