# Simple cross product

1. Oct 26, 2008

### jhicks

(This is part of a much larger problem)

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

Find $$\hat{r} \times \hat{z} \times \hat{y}$$

2. Relevant equations

$$x=rsin(\theta)cos(\phi)$$, $$y=rsin(\theta)sin(\phi)$$,$$z=rcos(\theta)$$ (cartesian->spherical)

3. The attempt at a solution

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

$$\hat{r} \times \hat{z} \times \hat{y}=\hat{r} \times (-\hat{x}) = -cos(\theta)\hat{y}+sin(\theta)sin(\phi)\hat{z}$$, but the solution to the problem suggests this is not true. Am I wrong?

2. Oct 27, 2008

### tiny-tim

Hi jhicks!

Do you mean r x (z x y) or (r x z) x y?

3. Oct 27, 2008

### jhicks

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!