Cross Product of Vector with Itself is Zero

Theorem
Let $\mathbf x$ be a vector in a vector space of $3$ dimensions:
 * $\mathbf x = x_i \mathbf i + x_j \mathbf j + x_k \mathbf k$

Then:
 * $\mathbf x \times \mathbf x = \mathbf 0$

where $\times$ denotes vector cross product.