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## 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?