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Expressing a circle in the form r(t) = x(t)i + y(t)i +z(t)k

  1. Jan 7, 2009 #1
    I learnt all the hard (at my level) bits like grad, div, curl and now I'm falling at the first hurdle on the exam papers:

    The question is: Express the circle of radius 3, centred at (1,0,3) and lying in the (x,z) plane in the form of r(t) = x(t)i + y(t)j + z(t)k

    I was hoping there was someone who wouldn't mind taking me through this step by step especially if there is a simple general equation as I have looked everywhere. And also what to do if it is in the other planes etc.

    Thank you,


    P.s. Sorry if this qualifies as homework, I thought that it didn't.
  2. jcsd
  3. Jan 7, 2009 #2


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    x(t)=3(cos(t) - 1)
    z(t)=3(sin(t) - 3)

    When the circle is in a plane perpendicular to one of the axes, it is easy as you can see.

    For the general case, it is more complicated. You can set it up in a coordinate system in the given plane and then transform into the global coordinates.
  4. Jan 8, 2009 #3
    :approve: Thanks alot, I don't think i'll be needing anything more complicated than this so greatly appreciated.

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