Theorem. Let $B_k$ be a symmetric matrix. Let $B_{k+1} = B_k+C$ where $C \neq 0$ is a matrix of rank one. Assume that $B_{k+1}$ is symmetric, $B_{k+1}s_{k} = y_k$ and $(y_{k}-B_{k}s_{k})^{T}s_{k} \neq 0$. Note that $s_k = x_{k+1}-x_k$. Then $C = \frac{(y_{k}-B_{k}s_{k})(y_{k}-B_{k}s_{k})^{T}}{(y_{k}-B_{k}s_{k})^{T}s_{k}}$
We know that $C = \gamma ww^{T}$ where $\gamma$ is a scalar and $w$ is a vector of norm $1$. Ultimately I get to the step that $\gamma(w^{T}s_{k})w = y_{k}-B_{k}s_{k}$
If $w \neq 0$, why does this imply that $w = \theta(y_{k}-B_{k}s_{k})$ where $\theta = \frac{1}{\|y_{k}-B_{k}s_{k}\|}$