1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Anti-Commutative Law

  1. Apr 26, 2007 #1
    Prove that anti-commutative law for the cross product: a * b = -(b * a)

    The question looks easy enough except that I can not find a definition of the anti-commutative law anywhere.

    I can find countless references to it but not a single definition. Can some one give me a run down on what the law entails?

    Thanks
     
  2. jcsd
  3. Apr 26, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You wrote out the definition in the first line. * is anticommutative if a*b=-b*a for all a,b.
     
  4. Apr 26, 2007 #3

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The law is directly stated in the question!!
    It just says that if you reverse the order of the two vectors, you get minus one times the original result.

    In genreal, consider an operation "F" that takes two quantities a and b as input and spits out a certain result. Let's write this as F[a,b] = R
    (the result R could be a number, a vector, a matrix, whatever).
    Is this function is antimmutative, it means that

    F[b,a] = - F[a,b]

    The dot product is commutative (switching the order of the two vectors multiplied gives the same result) whereas the cross product is anticommutative. Of course, a general function of two arguments does not have to be either commutative or anticommutative.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Anti-Commutative Law
  1. Almost commutative (Replies: 2)

  2. Commutator subgroup. (Replies: 1)

  3. Operators commute? (Replies: 6)

Loading...