A property of bilinear form

Question

in $E=\mathbb{R}^n$, $u:E\to E$ is linear positive symmetric. $E = (e_1,...e_n)$is a orthonormal basis. Define a bilinear form $q(x)=<x,u(x)>$.

Prove that:

There exists a basis $B=(b_1,...,b_n)$ s.t. $\forall i\in[n]$, $q(b_i)=0$ $\Leftrightarrow$ $\sum_{k=1}^n q(e_n)=0$

I have no idea from right to left, someone could help me?

Thanks a lot~