Simple cross product

  • Thread starter jhicks
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  • #1
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(This is part of a much larger problem)

Homework Statement



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

Homework Equations



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

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?
 

Answers and Replies

  • #2
tiny-tim
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Find [tex]\hat{r} \times \hat{z} \times \hat{y}[/tex]

Hi jhicks! :smile:

Do you mean r x (z x y) or (r x z) x y? :confused:
 
  • #3
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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.

Thanks!
 

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