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Vector Dot/Cross Identity

  1. Mar 6, 2010 #1
    Hi, I was looking at an EM problem today and realized I wasn't sure why

    (kxH)[tex]\dot[/tex]k = 0

    I tried writing it out explicitly and got (w 1,2,3 representing directions)

    A1(A2*B3-A3*B2) - A2(A1*B3-A3*B1) + A3(A1*B2-A2*B1)

    and I can't see why this should equal zero. This is troubling because the whole dot product of a cross product where one of the vectors is repeated seems to be a general result (of course AxA = 0, that is fine). In fact, I realized I have been using it fairly frequently and wasn't sure why it was so. Any help would be appreciated.
  2. jcsd
  3. Mar 6, 2010 #2


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    Well wouldn't kxH give a vector that is perpendicular to both k and H? That vector dot product with k wouild give what then?
  4. Mar 6, 2010 #3
    damn it, i knew it was something that simple. of course the result of the curl operation will be a vector quantity that is perpendicular to both k and H. Then the dot product of perpendicular vectors is zero. Thanks for kicking me in the head ;D
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