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Homework Help: Cylindrical coordinates of line through a point?

  1. Mar 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis.

    2. Relevant equations

    How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful.

    3. The attempt at a solution

    The z-axis is (0,0,1) while the cylindrical coordinates are (√2, ∏/4, z)

    Now, is the solution in the form of and r = (√2, ∏/4, 0) + (0,0,1)t? Or am I completely lost? (haha)
    Last edited: Mar 8, 2013
  2. jcsd
  3. Mar 8, 2013 #2

    rude man

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    Draw a line r from the origin to the line x = 1 at some point y. Connect that point with a line r going to the origin.
    What is r(y)? Or - hint - r2(y)?
    Then, can you express θ in terms of y?
    Finally you wind up with f(r) = (const.) + g(θ).

    EDIT: oh dear, I assumed the line parallel to the y axis. Never mind ...
    Last edited: Mar 8, 2013
  4. Mar 8, 2013 #3


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    hi whig4life! :smile:
    sorry to be pernickety, but no, (0,0,1) is a point, isn't it? :wink:

    correct :smile:
    it depends whether you want a parametric equation or an ordinary one

    the ordinary equation is r = √2, θ = ∏/4

    (just as in cartesian coordinates it would be x = y = 1)

    the parametric equation is not (r,θ,z) = (√2, ∏/4, 0) + (0,0,1)t

    you can't add non-cartesian coordinates (try adding (1,0,0) to (1,∏,0) … do you get (2,∏,0) ?)

    it's (r,θ,z) = (√2, ∏/4, …?… ) ?
  5. Mar 8, 2013 #4
    I was told: The answer should probably be given in parametric form

    r = something, theta = something, z = something

    So, any ideas? I've exhausted all my resources trying to look for this maybe a better mind can see it more clearly.
    Last edited: Mar 8, 2013
  6. Mar 9, 2013 #5


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    hi whig4life! :smile:

    (just got up :zzz:)

    the parametric equation would be r = √2, θ = ∏/4, z = … ?
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