(α1,β)=0 ,(α2,β)=0 and so on .A equation about Vector β can display β=X1α1+X2α2+...Xnαn ,because a series of above vectors are linear independence .You make (β,β)=X1(β,α1)+X2(β,α2)+...Xn(β,αn),pay more attention this is called Distribution Law.(β,β)=0 can be deduced with ease.make use of if and only if you get β=null vector.