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Cross product of polar coordinates

  1. May 18, 2005 #1
    When using cartesian coordinates, I use the following expressions to calculate the cross product of the basis vectors:

    [tex]i \times j = k[/tex]
    [tex]j \times k = i[/tex]
    [tex]k \times i = j[/tex]
    [tex]j \times i = -k[/tex]
    [tex]k \times j = -i[/tex]
    [tex]i \times k = -j[/tex]

    Can I do the same in polar coordinates? How could I write the cross product for the vectors [tex]r[/tex], [tex]\theta[/tex] and [tex]z[/tex]?
    Last edited: May 18, 2005
  2. jcsd
  3. May 18, 2005 #2


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    Yep, the right-hand version is [tex]\vec{i}_{r}\times\vec{i}_{\theta}=\vec{k}[/tex]
    and you can complete the cycle from there..
  4. May 18, 2005 #3


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    The cylidrical coordinates are orthogonal,which means that the basis vectors are orthogonal to each other,too.They can be made to form a rectangular trihedron,just like [itex] \vec{i},\vec{j} \ \mbox{and} \ \vec{k} [/itex].

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