Differential Equation: Cross product Query

**bugatti79** · November 20th 2010, 07:45 AM

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

**FernandoRevilla** · November 20th 2010, 08:20 AM

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

Regards.

Fernando Revilla

**bugatti79** · November 21st 2010, 05:06 AM

Originally Posted by FernandoRevilla

If $\nabla (\phi)=(2x,2y,2u)$ and $\nabla ( \psi)=(0,0,1)$ then, $\nabla (\phi)\times \nabla ( \psi)=(2y,-2x,0)$ and this means that $\nabla (\phi)\times \nabla ( \psi)$ 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

**Ackbeet** · November 22nd 2010, 05:36 AM

Looks good to me.

Thread: Differential Equation: Cross product Query

LinkBack

Thread Tools

Display

Differential Equation: Cross product Query

Similar Math Help Forum Discussions

Cross product

[SOLVED] 2nd differential query?

finding angle using cross product and dot product

Cross product and dot product relationships

Vectors, dot product and cross product. URGENT please Help