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## Homework Statement

I have repeated this problem over and over again so either the question is wrong or my likely its my method that's at fault. Please can someone check this for me.

Prove this is true:

[tex]\nabla\times(\nabla \times F)=-\nabla^{2}F+\nabla(\nabla.F)[/tex]

for [tex]F=x^{2}z^{3}i[/tex]

## The Attempt at a Solution

Im getting for the LHS:

[tex](\nabla \times F)= 3x^{2}z^{3} j[/tex]

[tex]\nabla\times(\nabla \times F)= -6x^{2}z i + 6xz^{2}k[/tex]

and for the right:

[tex]-\nabla^{2}F=-2z^{3} i[/tex]

[tex](\nabla.F)=2xz^{3}[/tex]

[tex]\nabla(\nabla.F)=2z^{3}i + 6xz^2k[/tex]

[tex]-\nabla^{2}F+\nabla(\nabla.F)=6xz^{2} k[/tex]

[tex]\Rightarrow \nabla\times(\nabla \times F)\neq-\nabla^{2}F+\nabla(\nabla.F)[/tex]

for [tex]F=x^{2}z^{3}i[/tex]