# Vectors in R^n

• January 13th 2008, 10:21 AM
In $R^n , n \geq 2$
a) Prove that there exist $(x_{1}, . . . , x_{n+1} ) \in R^n$
b) $|x_{i}| = 1 \ \ \ \ \ i = 1 , 2 , 3 , . . . , n$
$(x_{i} \cdot x_{j} ) = \alpha _{n} , i \neq j , i,j = 1 ,2 , . . . , n$, what is $\alpha _{n} =$ ?