# How can the angle between A×B and B×A be 180 degrees?

Jun 30, 2018

${\underbrace{\boldsymbol{A} \times \boldsymbol{B}}}_{{V}_{1}} = - {\underbrace{\boldsymbol{B} \times \boldsymbol{A}}}_{{V}_{2}}$

ie ${V}_{1}$ and ${V}_{2}$ are anti-parallel vectors.

If you look at the definition of the vector product:

• $\boldsymbol{A} \times \boldsymbol{B} = \left\mid \boldsymbol{A} \right\mid \left\mid \boldsymbol{B} \right\mid \sin {\theta}_{A B} \setminus \boldsymbol{\hat{n}}$

• $\boldsymbol{B} \times \boldsymbol{A} = \left\mid \boldsymbol{A} \right\mid \left\mid \boldsymbol{B} \right\mid \sin {\theta}_{B A} \setminus \boldsymbol{\hat{n}} '$

And

• ${\theta}_{A B} = {\theta}_{B A}$

But because of the operation of the Right hand rule, $\hat{\boldsymbol{n}}$ and $\hat{\boldsymbol{n}} '$ are anti parallel.