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I Cross product

  1. May 6, 2016 #1
    Is there any proof for the matrixx formula of the cross product. I am asking this because I have seen many videos and they have used the matrixx formula and then proved that ||A X B|| = ||A|||B||sin(theta), khan academy also used the same method
     
  2. jcsd
  3. May 6, 2016 #2

    fresh_42

    Staff: Mentor

    What do you mean by "matrixx formula"?
     
  4. May 6, 2016 #3

    jedishrfu

    Staff: Mentor

    The matrix formula aka the cross product determinant is more of a mnemonic device to help you compute the cross product in a Cartesian coordinate system.

    from wikipedia (see the matrix notation and the Sarrus' Rule:

    https://en.wikipedia.org/wiki/Cross_product
     
  5. May 6, 2016 #4
    See jedishrfu answer
     
  6. May 6, 2016 #5

    jedishrfu

    Staff: Mentor

  7. May 6, 2016 #6

    Mark44

    Staff: Mentor

    Sorry, this isn't the definition of the cross product A x B. It's the definition of the magnitude or norm of A x B; i.e., |A x B|.
    In the pdf in the link, the author never gives a geometric definition of the cross product. This product could be defined as A x B = (|A||B| sin(θ)) u, where u is a unit vector that is perpendicular to both A and B. The orientation of u can be determined using the right-hand rule (i.e., if you let the fingers of your right hand curl around from A to B, your thumb will point in the direction of u).
     
  8. May 6, 2016 #7

    jedishrfu

    Staff: Mentor

    My apologies I forgot to mention that the resultant vector is perpendicular to both A and B and follows the right-hand rule for direction as determined via rotation from A to B.

    Alas, still learning what I forgot and forgetting what I've I've relearned.
     
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