Originally Posted by

**backflip** Hi, just need a quick hand on an assignment question:

What I've done so far is (convert to spherical) parameterise $\displaystyle S$ by $\displaystyle r(\theta,\phi)=5sin{\phi}cos{\theta}i+5sin{\phi}si n{\theta}j+5cos{\phi}k$

And taken the vectors $\displaystyle r_\theta$ and $\displaystyle r_\phi$, found their cross product as a normal vector, then taken the dot product with $\displaystyle F$.

What results is something horrible (seeing as the integral must be taken), and it makes me think that something has gone very wrong:

$\displaystyle F \cdot (r_\theta \times r_\phi) =625sin^3{\phi}cos{\phi}cos^2{\theta}+125sin^3{\ph i}sin{\theta}cos{\theta}+125sin^2{\phi}cos{\phi}si n{\theta}$

Obviously I'm not looking for an answer to the problem, but I'm pretty sure that I've made an error somewhere, and I would appreciate it if someone could point it out. More details of the in-between steps can be supplied, if needed.

Thanks in advance.