How can the angle between A×B and B×A be 180 degrees?
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'#
#theta_(AB) = theta_(BA)#
But because of the operation of the Right hand rule,