Let $V$ and $V^{\prime}$ be two subspaces of $E$ of dimension $p$. Let $u = (u_1, \ldots, u_p)$ and $u^{\prime} = (u_1^{\prime}, \ldots, u_p^{\prime})$ be the orthonormal families constructed in question (1).
Show that if $\operatorname{dim}(V \cap V^{\prime}) \geqslant 1$, then $u_k = u_k^{\prime}$ for all $1 \leqslant k \leqslant \operatorname{dim}(V \cap V^{\prime})$.