Problem
Problem 6.76 Let $(M, g)$ be a Riemannian $n$-manifold. Consider an orthonormal basis $\left\{e_{1}, \ldots, e_{n-1}, X\right\}$ of $T_{p} M, p \in M$. Let $P_{i}$ be the plane section generated by $e_{i}$ and $X ; K\left(P_{i}\right)$ the sectional curvature of $P_{i} ;$ and $\mathbf{r}$ the Ricci tensor. Prove that
$$
\mathbf{r}(X, X)=\sum_{i=1}^{n-1} K\left(P_{i}\right)
$$