Vector Cross Product satisfies Jacobi Identity

Theorem
Let $\mathbf a, \mathbf b, \mathbf c$ be vectors in $3$ dimensional Euclidean space.

Let $\times$ denotes the cross product.

Then:
 * $\mathbf a \times \paren {\mathbf b \times \mathbf c} + \mathbf b \times \paren {\mathbf c \times \mathbf a} + \mathbf c \times \paren {\mathbf a \times \mathbf b} = \mathbf 0$

That is, the cross product operation satisfies the Jacobi identity.