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Simple cross product

  1. Oct 26, 2008 #1
    (This is part of a much larger problem)

    1. The problem statement, all variables and given/known data

    Find [tex]\hat{r} \times \hat{z} \times \hat{y}[/tex]

    2. Relevant equations

    [tex]x=rsin(\theta)cos(\phi)[/tex], [tex]y=rsin(\theta)sin(\phi)[/tex],[tex]z=rcos(\theta)[/tex] (cartesian->spherical)

    3. The attempt at a solution

    I decided [tex]\hat{r}=\hat{x}sin(\theta)cos(\phi)+\hat{y}sin(\theta)sin(\phi)+\hat{z}cos(\theta)[/tex]. Evaluating the cross product right to left, I got:

    [tex]\hat{r} \times \hat{z} \times \hat{y}=\hat{r} \times (-\hat{x}) = -cos(\theta)\hat{y}+sin(\theta)sin(\phi)\hat{z}[/tex], but the solution to the problem suggests this is not true. Am I wrong?
  2. jcsd
  3. Oct 27, 2008 #2


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    Hi jhicks! :smile:

    Do you mean r x (z x y) or (r x z) x y? :confused:
  4. Oct 27, 2008 #3
    Hi tiny-tim,

    Well there're no parentheses in the problem, but somehow when I did this last night I concluded you evaluate cross products right to left, but I see the error of my ways.

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