Show that, given two tangent vectors $V$ and $W$ of a hypersurface $\Sigma$, contraction with the projection tensor $P_{\mu u}$ reduces to a scalar product:

$$\begin{equation*}
P_{\mu u} V^{\mu} W^{u}=g_{\mu u} V^{\mu} V^{u}=V \cdot W . \tag{5.400}
\end{equation*}$$