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How do you prove that a=-(w^2)

  1. Feb 6, 2006 #1
    how do you prove that a=-(w^2)
    from v=wxr?
    i know you're supposed to differentiate v=wxr, but i don't know how to differentiate a cross product...
     
    Last edited by a moderator: Jan 7, 2014
  2. jcsd
  3. Feb 6, 2006 #2
    The cross product is the vector created by the determinant
    [tex] a \times b =
    \begin{tabular}{|c c c|}
    i & j & k \\
    a_1 & a_2 & a_3 \\
    b_1 & b_2 & b_3 \\
    \end{tabular}
    [/tex]

    So, take the determinant of the above matrix, and then differentiate as normal. (Hint: the determinant will give you a vector, with 3 coordinates. You can differentiate each coordinate on its own.)

    Edit: are you familiar with how to take a determinant? Otherwise you can use [itex]a \times b = |a||b|\sin{\theta}[/itex], but then you'll have to know [itex]\theta[/itex], or treat it as a constant.
     
    Last edited: Feb 6, 2006
  4. Feb 7, 2006 #3
    wow!
    thank you very much!!!
    what happens if you want to prove it for an infinite number of coordinates(ex., i, j, k, l, m, ....)?
     
  5. Feb 7, 2006 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The cross product is only defined in R3.
     
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