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Vector Product

  1. Sep 2, 2010 #1
    Given two vectors p and q, why is the vector (cross) product pxq perpendicular to the plane containing these vectors?
    Is there a geometric or physical way of explaining why?
    Are there any real life examples we can draw from?
     
  2. jcsd
  3. Sep 4, 2010 #2

    Landau

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    Well, what is your definition of cross product? Sometimes this (perpendicularity) is part of the definition.
     
  4. Sep 4, 2010 #3
    Two links posted recently in these forums are online introductions to multivariable calculus which each contain a chapter relating the algebraic expression for the components of a cross product to the property of being perpendicular to its factors:

    http://synechism.org/drupal/cfsv/
    http://www.owlnet.rice.edu/~fjones/

    Greg Egan used to have a nice demonstration of the correspondence between geometric and componentwise definitions of the dot product (which is taken as the starting point by the links above), but I can't seem to find it now. Never mind, Google knows lots more. You can shop around for the one that makes most sense to you.
     
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