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Show a flowline of a vector field?

  1. Mar 7, 2012 #1

    Suy

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    Show a flowline of a vector field??

    1. The problem statement, all variables and given/known data

    Consider the vector field F(x,y,z)=(8y,8x,2z).
    Show that r(t)=(e8t+e−8t, e8t−e−8t, e2t) is a flowline for the vector field F.

    r'(t)=F(r(t)) = (_,_,_)

    Now consider the curve r(t)=(cos(8t), sin(8t), e2t) . It is not a flowline of the vector field F, but of a vector field G which differs in definition from F only slightly.

    G(x,y,z)=(_,_,_)

    2. Relevant equations

    3. The attempt at a solution

    I guess the first part of the question r'(t)=F(r(t)) = (8e8t-8e-8t,8e8t-8e-8t,2e2t)

    For the second part, I don't understand the question... hope someone can explain to me?
     
  2. jcsd
  3. Mar 7, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Show a flowline of a vector field??

    Okay, and do you understand why that is "(8y, 8x, 2z)"?

    Do the same thing. If [itex]r(t)= (x, y, z)= (cos(8t), sin(8t), e^{2t})[/itex] what is [itex]r'(t)[/itex]? What is that in terms of x, y, and z?
     
  4. Mar 7, 2012 #3

    Suy

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    Re: Show a flowline of a vector field??

    Thanks for the reply!! It definitely helped me understanding the question!!! And I know how to do it now!
     
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