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How to find the unit vector in cylindrical coordinates

  1. May 30, 2010 #1
    So i'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?
     
  2. jcsd
  3. May 30, 2010 #2
    The cylindrical unit vector is er.
    x/|x|
    Where x is where ever we are. (not cartesian x)

    x=r(e_r)+z(e_z)
    and |x|^2 = x.x

    I think that works. Sorry about not underlining vectors.

    e_r can be expressed in terms of e_x and e_y and some trig things.
     
  4. May 30, 2010 #3
    Here is my understanding,

    Given a unit vector A = x1,y1,z1 in cartesian, to transform into cylindrical just use the transform
    A . [tex]\rho[/tex]
    A . [tex]\phi[/tex]
    Z(cartesian)=Z(cylindrical)

    my question is, since x . [tex]\rho[/tex] = cos[tex]\phi[/tex], is the [tex]\phi[/tex] that I am supposed to use the tan^-1(y1/X1)?

    If this is the case then I don't understand what the solutions manual did with the following problem
    problem18.jpg
    I understand part a.) but in part b.) they use 70 degrees as [tex]\phi[/tex] when according to part a.), [tex]\phi[/tex] should be -89 degrees. Am I missing something?
     
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