(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A vector fieldFfor which divF= 0, is called incompressible (also called solenoidal). Consider the vector fieldF(x, y, z) = ⟨y, x + y, −z⟩.

(a) (1 point) Show thatFis incompressible.

(b) (3 points) Find a vector fieldAsuch thatF=[tex]\nabla[/tex]×A.

2. Relevant equations

divF= [tex]\nabla[/tex] .F

3. The attempt at a solution

I understand how to do part a and confirmed that divF= 0 and thus is incompressible.

But I'm not entirely sure how to find part b.

Is there a cross product operation in whichA= some combination ofFand [tex]\nabla[/tex]?

Or would you assignAsome arbitrary vectors [tex]\left\langle[/tex]P,Q,R⟩ and take the cross of those with [tex]\nabla[/tex]. Resulting in the vector

⟨y, x + y, −z⟩ = (dR/dy-dQ/dz)i-(dR/dx-dP/dz)j+(dQ/dx-dP/dy)k

and somehow solve for P,Q,R?

Or am I completely on the wrong track?

Any help or advice would be wonderful!

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# Homework Help: Divergence and F=∇×A

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