We consider the three vectors
$$w_1 = \begin{pmatrix}0\\1\\0\end{pmatrix}, \quad w_2 = \begin{pmatrix}1\\-1\\0\end{pmatrix}, \quad w_3 = \begin{pmatrix}-1\\0\\-1\end{pmatrix}.$$
We denote by $T$ the set of vectors $v\in\mathcal{H}$ such that $B(v,w_i)\geq 0$ for all $i\in\{1,2,3\}$.
Show that $T$ is compact and contains $v_0 = \begin{pmatrix}0\\0\\1\end{pmatrix}$.