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Homework Help: HELP - continuity

  1. Dec 5, 2008 #1
    1. Show that the cross product is a continuous function

    I have tried to apply the definition of continuity: find a delta such that
    |x-y|< delta implies |f(x)-f(y)|< epsilon
    but I'm having trouble finding a delta that would take me to the conclusion.
  2. jcsd
  3. Dec 5, 2008 #2


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    Perhaps you should show us what you've tried. What is |f(x)-f(y)| in this case?
  4. Dec 5, 2008 #3
    In this case, |f(x)-f(y)| is a real number (the length of a vector in R^3).
    A better question is what is |x-y|. x is one pair of vectors in R^3 and y is another pair of vectors in R^3. Then what is |x-y|?
    I have tried relating |x-y| to the fact that |a x b|=|a||b|sin(theta) but can't get anything that seems to be on the right direction.
  5. Dec 7, 2008 #4
    I figured it out.
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