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Basic Vector Calculus

  1. Mar 3, 2009 #1
    Hi all,

    Would someone please re-enlighten me.

    Say I have a vector in spherical coordinates:

    [tex]\vec r_1 = \phi \hat{\phi} + \theta \hat{\theta} + R \hat{R}[/tex]

    Where [tex] r, \theta, R [/tex] are scalars and the corresponding hat notation is the unit vectors.

    Say, I form a new vector [tex] r_2 [/tex] in spherical coordinates.

    Would the distance from r_1 to r_2 be given by the norm of r_2-r_1.


    What I'm trying to ask is this:
    1) In rectangular coordinates I can find the vector from one point to another, via V_ab = V_b - V_a
    2) If I have two vectors in spherical coordinates, can I find the distance from one point to another with subtraction? Or do I need to convert the spherical vectors to rectangular, and then perform the subtraction.
     
  2. jcsd
  3. Mar 4, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi FrogPad! :smile:
    Your suspicion is correct … you certanily can't use subtraction. :smile:

    Either convert to rectangular, or use the cosine rule:

    r122 = r12 + r22 - 2r1r2cosθ,

    where in two dimensions θ = θ1 - θ2, but in three dimensions θ is a lot more complicated! :rolleyes: :frown: :wink:
     
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