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Operations on 2 vector fields?

  1. Nov 16, 2007 #1
    Supposing we have as 2 vector fields:

    [tex] F = x^2i + 2zj +3k [/tex]
    and
    [tex] G = r^2e_r + 2\cos\Theta e_{\Theta} + 3\sin(2\phi) e_\phi [/tex]

    how do i perform the following operations on them?

    - [tex] F\cdot r [/tex]

    - [tex] F\times r [/tex]

    - |G|

    - [tex] G\cdot r [/tex]
     
  2. jcsd
  3. Nov 16, 2007 #2

    robphy

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    Can you write [tex]\hat r[/tex] in terms of rectangular components and of spherical-polar coordinates?
     
    Last edited: Nov 16, 2007
  4. Nov 20, 2007 #3


    No, sorry. How do i do that??
     
  5. Nov 20, 2007 #4
    Suppose that you are in three dimensions. You can use standard Cartesian coordinates [itex](x,y,z)[/itex] or spherical polar coordinates [itex](r,\theta,\phi)[/itex] to describe this three-dimensional space in a convenient manner.

    To begin finding a solution to your problem, how are the coordinates [itex](r,\theta,\phi)[/itex] related to the coordinates [itex](x,y,z)[/itex]?

    Now how are the basis vectors [itex]\{\hat{e}_x,\hat{e}_y,\hat{e}_z\}[/itex] for the Cartesian coordinate system related to the basis vectors [itex]\{\hat{e}_r,\hat{e}_\theta,\hat{e}_\phi\}[/itex] of the spherical polar coordinate system?
     
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