Question

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

Answer 1

`underbrace(bbA times bbB)_(V_1) = - underbrace(bbB times bbA)_(V_2)`

ie `V_1` and `V_2` are anti-parallel vectors.

If you look at the definition of the vector product:

• `bbA times bbB = abs bbA abs bbB sin theta_(A B) \ bbhatn`

• `bbB times bbA = abs bbA abs bbB sin theta_(B A) \ bbhatn'`

And

• `theta_(AB) = theta_(BA)`

But because of the operation of the Right hand rule, `hatbbn` and `hatbbn'` are anti parallel.

Wikipedia