# Vector identites question

• Nov 16th 2013, 06:32 AM
MathGeni04
Vector identites question
prove that

Δ.(ΨΔφ x φΔΨ)=0
where Δ is delta.
anybody help plz
• Nov 16th 2013, 02:41 PM
chiro
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.
• Nov 16th 2013, 03:11 PM
Plato
Re: Vector identites question
Quote:

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?
• Nov 18th 2013, 07:18 PM
MathGeni04
Re: Vector identites question
\Delta is del operator.
• Jan 5th 2014, 05:58 AM
Pete
Re: Vector identites question
Quote:

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?
• Jan 6th 2014, 06:22 AM
HallsofIvy
Re: Vector identites question
So you really mean "$\displaystyle \nabla \cdot ((\nabla \psi)\phi \times \psi(\nabla\phi))= 0$"?
• Jan 8th 2014, 08:45 AM
Pete
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.