Vector Cross Product is Anticommutative/Proof 4

Proof
From the definition of the vector cross product:

Hence we have that:
 * $\mathbf a \times \mathbf b$ is a vector whose direction is specified according to the right-hand rule

while:
 * $\mathbf b \times \mathbf a$ is a vector whose direction, also specified according to the right-hand rule, is exactly the opposite of that for $\mathbf a \times \mathbf b$.

That is:
 * $\mathbf a \times \mathbf b = -\mathbf b \times \mathbf a$