1. ## Vector identites question

prove that

Δ.(ΨΔφ x φΔΨ)=0
where Δ is delta.
anybody help plz

2. ## Re: Vector identites question

Hey mathgeni04.

Hint: Expand all the vectors out in terms of <x,y,z> terms and use the definition of the dot and cross products.

3. ## Re: Vector identites question

Originally Posted by MathGeni04
prove that
Δ.(ΨΔφ x φΔΨ)=0
where Δ is delta.
anybody help plz
I do not disagree with reply #2 but I do wonder if by $\displaystyle \Delta$ you really mean $\displaystyle \nabla =i \frac{\partial }{{\partial x}} +j \frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}~?$

That is 'nabla' or the del operator. If not what does $\displaystyle \Delta$ mean?

4. ## Re: Vector identites question

\Delta is del operator.

5. ## Re: Vector identites question

Originally Posted by MathGeni04
prove that

Δ.(ΨΔφ x φΔΨ)=0
where Δ is delta.
anybody help plz
I'm confused here. If φ and Ψ are functions then what does the operator x represent if not simple multiplication?

6. ## Re: Vector identites question

So you really mean "$\displaystyle \nabla \cdot ((\nabla \psi)\phi \times \psi(\nabla\phi))= 0$"?

7. ## Re: Vector identites question

Thanks HallsofIvy. If that were the case then the whole thing makes sense, if it's an actual identity that is.