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

1 Answer
Jun 30, 2018

#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.

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