$M$ is an Riemannian n-manifold, $p\in M$. $x, y\in T_pM$. Is it true that $\langle x,x \rangle \langle y, y \rangle-\langle x, y \rangle^2=|x \wedge y|^2$?
I'm reading Do Carmo's Riemannian geometry and I don't quite understand how the wedge product is defined for tangent vectors and how it interacts with inner product.