**Surface Integrals and Flux in Vector Fields**5. The surface integral for a vector field contains the term:\[ F \cdot (r_u \times r_v) \]for a vector field $ F $ and parametrization $ r(u, v) $. This arises from a sum that contains the term:\[ F \cdot (r_u \times r_v)\Delta u \Delta v. \]Now imagine that $ F $ is the velocity field of a fluid moving across the surface $ S $. Give a geometric interpretation of this triple product term and use this to explain the term "Flux" used to describe the surface integral of a vector field.

5. The surface integral for a vector field contains the term F. (ru x Tv) for a vector field F and parametrization r(u, v). This arises from a sum that contains the term F. (ru xry)ΔuΔυ. 1 Now imagine that F is the velocity field of a fluid moving across the surface S. Give a geometric interpretation of this triple product term and use this to explain the term "Flux" used to describe the surface integral of a vector field.

5. The surface integral for a vector field contains the term F. (ru x Tv) for a vector field F and parametrization r(u, v). This arises from a sum that contains the term F. (ru xry)ΔuΔυ. 1 Now imagine that F is the velocity field of a fluid moving across the surface S. Give a geometric interpretation of this triple product term and use this to explain the term "Flux" used to describe the surface integral of a vector field.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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**Surface Integrals and Flux in Vector Fields**

5. The surface integral for a vector field contains the term:

\[ F \cdot (r_u \times r_v) \]

for a vector field $ F $ and parametrization $ r(u, v) $. This arises from a sum that contains the term:

\[ F \cdot (r_u \times r_v)\Delta u \Delta v. \]

Now imagine that $ F $ is the velocity field of a fluid moving across the surface $ S $. Give a geometric interpretation of this triple product term and use this to explain the term "Flux" used to describe the surface integral of a vector field.

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Step 1: Required to give the geometric interpretation of the triple product.

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