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:
 * $\mathbf a \times \left(\mathbf b \times \mathbf c\right) + \mathbf b \times \left(\mathbf c \times \mathbf a\right) + \mathbf c \times \left(\mathbf a \times \mathbf b\right) = \mathbf 0$

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