# Thread: Differential Equation: Cross product Query

1. ## Differential Equation: Cross product Query

Can anyone check I have calculated correctly the cross product of 2 vectors..
See attached.
It is part of a problem to solve a quasi linear equation in which a horizontal plane cuts a sphere.
I am to check that the 2 functions phi and psi are linearly independent if there cross product is not equal to 0. Although it a very simple problem, I havent come across it before.

Thanks

2. If $\displaystyle \nabla (\phi)=(2x,2y,2u)$ and $\displaystyle \nabla ( \psi)=(0,0,1)$ then, $\displaystyle \nabla (\phi)\times \nabla ( \psi)=(2y,-2x,0)$ and this means that $\displaystyle \nabla (\phi)\times \nabla ( \psi)$ is different from the null vector field.

Regards.

Fernando Revilla

3. Originally Posted by FernandoRevilla
If $\displaystyle \nabla (\phi)=(2x,2y,2u)$ and $\displaystyle \nabla ( \psi)=(0,0,1)$ then, $\displaystyle \nabla (\phi)\times \nabla ( \psi)=(2y,-2x,0)$ and this means that $\displaystyle \nabla (\phi)\times \nabla ( \psi)$ is different from the null vector field.

Regards.

Fernando Revilla
ok, I think I know where you got it from. Can you check i derived it properly? See attached. Thanks

4. Looks good to me.