1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper
    Gold Member

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi whig4life! :smile:

    (just got up :zzz:)

    the parametric equation would be r = √2, θ = ∏/4, z = … ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted