Explanation Given: F is the incompressible vector field and it being tangent to the surfaces of f . Calculation: As the F is the incompressible vector field, the divergent of F is equal to zero. Here, f is the scalar field. Apply product rule of divergent as follows: D i v ( f F ) = f D i v ( F ) + ∇ f ⋅ F D i v ( f F ) = 0 + ∇ f ⋅ F As the f is the scalar function, then gradient of scalar gives vector field which is normal to the surface

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ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.3, Problem 33E

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To prove:

fF is incompressible.

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Chapter 17.3, Problem 32E

Chapter 17.3, Problem 34E

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Chapter 17 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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To prove: f F is incompressible.

Solution Summary: The author explains that F is the incompressible vector field and it being tangent to the surfaces of f.

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To prove:

fF is incompressible.

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Chapter 17 Solutions

To prove: f F is incompressible.

Solution Summary: The author explains that F is the incompressible vector field and it being tangent to the surfaces of f.

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To prove: fF is incompressible.

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Chapter 17 Solutions

To prove:

fF is incompressible.