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Math Help - a calculus proof

  1. #1
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    a calculus proof

    prove that

    d/dt(rsub1(t) dot rsub2(t) ) = r'sub1(t) dot r'sub2(t) + rsub1(t) dot r'sub2(t)

    Thank you very much
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    The dot here means dot product right? cause if it meant multiply it wouldn't be a prob, it would just be the product rule.
    Last edited by Jhevon; February 22nd 2007 at 09:24 AM.
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  3. #3
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    Hi Jhevon,

    You are right. I got this part. It is actually very simple. Thank you very much.

    what about the below part :
    use
    d/dt(rsub1(t) dot rsub2(t) ) = r'sub1(t) dot r'sub2(t) + rsub1(t) dot r'sub2(t)
    to show that for a differentiable 3-space vector valued function r, the graph of r lies on a sphere centered at the orgin if and only if r(t) and r'(t) are orthogonal.
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  4. #4
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    If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.
    Taking the derivative we get R(t)R(t)/[R(t)R(t)]=0 or R(t)R(t)=0.
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