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Proving Vector Properties

  1. Jun 13, 2008 #1
    I can't seem to figure out how to prove the property for R(t) = <f(t), g(t), h(t)> :

    Dt[R(t) X R'(t)] = R(t) X R"(t)

    Any suggestions?!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jun 13, 2008 #2


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    Homework Helper

    is X cross product?
    [R(t) X R'(t)]' = R'(t) X R'(t)+R(t) X R"(t)
    for any sensible derivative
    [R(t) X R'(t)]' = R(t) X R"(t)
    if and only if
    R'(t) X R'(t)=0
    clearly true for cross product
  4. Jun 13, 2008 #3


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    Staff Emeritus
    Science Advisor

    Is the "Dt" derivative with respect to t? i.e.(R x R')' ?

    What have you tried? Have you tried actually writing out each side in terms of derivatives of f, g, and h?

    Do you know that the "product rule" from Calculus I is still true for vector products? What does that give you?
  5. Jun 13, 2008 #4
    wow.. I had copied the property [R(t) x R'(t)]' = blah blah blah.. incorrectly from my book... It makes perfect sense now, thank you for the help!!
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