In $\displaystyle R^n , n \geq 2 $

a) Prove that there exist $\displaystyle (x_{1}, . . . , x_{n+1} ) \in R^n $

b) $\displaystyle |x_{i}| = 1 \ \ \ \ \ i = 1 , 2 , 3 , . . . , n$

$\displaystyle (x_{i} \cdot x_{j} ) = \alpha _{n} , i \neq j , i,j = 1 ,2 , . . . , n $, what is $\displaystyle \alpha _{n} =$ ?

c) Prove that there is no (n+2) vectors.

I'm really sorry but I'm lost at this problem, to be honest, I don't even know what the professor is asking. He is Russian and I cannot understand what he is saying or writing...

Thank you.