- #1
SAMSAM12
- 2
- 0
Homework Statement
If [itex]\phi[/itex]= xy[itex]^{2}[/itex]
A=xzi-z[itex]^{2}[/itex]j+xy[itex]^{2}[/itex]k
B=zi+xj+yk
Verify that
[itex]\nabla[/itex].([itex]\phi[/itex]A)=A.[itex]\nabla[/itex][itex]\phi[/itex]+[itex]\phi[/itex].[itex]\nabla[/itex]A
Homework Equations
The Attempt at a Solution
I have worked out the first two parts of the question:
[itex]\phi[/itex]A = (x[itex]^{2}[/itex]y[itex]^{2}[/itex]z, -xy[itex]^{2}[/itex]z[itex]^{2}[/itex],x[itex]^{2}[/itex]y[itex]^{4}[/itex])
div([itex]\phi[/itex]A) = 2xy[itex]^{2}[/itex]z-2xyz[itex]^{2}[/itex]
A.grad([itex]\phi[/itex]) = (xy[itex]^{2}[/itex]z-2xyz[itex]^{2}[/itex])
I'm struggling to work out the last part:
[itex]\phi[/itex].[itex]\nabla[/itex]A
I tried working out [itex]\phi[/itex].grad(A)? but the answer sheet has
div(A) = z
[itex]\phi[/itex]div(A) = xy[itex]^{2}[/itex]z
why?
Any help appreciated.
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