What is the angle between A×B andB×A?

↳Redirected from "Question #99ee1"
1 Answer
Ultrilliam
Jun 8, 2018

See below

Explanation:

From the definition:

#bb A times bb B = abs bb A abs bb B sin alpha_("AB") \ bb hat n#

So #bb A times bb B# lies in the direction that is normal to both #bb A# and #bb B#, labelled #bb hat n#, and has magnitude #abs bb A abs bb B sin alpha_("AB")#, where #alpha_("AB")# is the angle between #bb A# and #bb B#

On the other hand:

#bb B times bb A = abs bb B abs bb A sin alpha_color(red)(bb "BA") \ bb hat n#

#= abs bb A abs bb B sin (-alpha_color(green)(bb "AB")) \ bb hat n#

#= bb color(red)(-) abs bb A abs bb B sin alpha_("AB") \ bb hat n#

IOW, these vectors have same magnitude, but are anti-parallel, so the angle between them is 180 degrees

It is therefore true to say that:

#bbA times bb B = - bb B times bb A#

And vice versa.

Related questions
Impact of this question
1712 views around the world
You can reuse this answer
Creative Commons License