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Homework Help: Parametric equations of line in 3D space

  1. Jan 1, 2010 #1
    Hello, sorry for my Englich:D
    1. The problem statement, all variables and given/known data
    I must count a line integral on the lenght which lies on the line which is defined by equations:
    [tex]\begin{cases}x^2+y^2+z^2=R^2\\ \left(x-\frac{R}{2}\right)^2+y^2=\left(\frac{R}{2}\right)^2\end{cases}[/tex]
    it is a column which is cutting a sphere
    3. The attempt at a solution
    I tried to assumption that [tex]x=t[/tex] and then depending on this find other functions [tex]y(t),z(t)[/tex], but the equations are not easy. I think I can find something with trigonometric functions sinus cosinus, but I am not sure; my question is then how I can easy and quickly find parametric equations of line which is make by two planes (in this case sphere and column) cutting each another? thanks for help!
    Last edited: Jan 1, 2010
  2. jcsd
  3. Jan 1, 2010 #2


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    Hello player1_1_1! :smile:

    (have a theta: θ and try using the X2 tag just above the Reply box :wink:)

    It's much better to have a single-valued parameter, which x isn't.

    So try using the angle (from the axis of the cylinder) as the parameter. :smile:

    (btw, we say "sine" and "cosine", and we usually say "curve" for a line that isn't straight … even though we say "line integral" for any curve! :rolleyes: :wink:)
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