Vector Identities: Calculate \nabla \cdot (f \nabla \times (f F))

In summary, the conversation is about using vector identities to calculate a specific equation involving a vector F and its magnitude f. The person is having trouble with this concept and is looking for help. They mention a book, "Vector Analysis and an Introduction to Tensor Analysis" by Murray R. Spiegel, as a helpful resource.
  • #1
Monster007
26
1
Vector Identities ??

Having heaps of trouble with v.identities any help possible would be greatly appreciated.

Let F = (z,y,-x) and f = |F| <--- (magnitude F)

Use vector identities to calculate;


\nabla \cdot (f \nabla \times (f F))

 
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  • #2


Monster007 said:
Having heaps of trouble with v.identities any help possible would be greatly appreciated.

Let F = (z,y,-x) and f = |F| <--- (magnitude F)

Use vector identities to calculate;

[tex]
\nabla \cdot (f \nabla \times (f F))

[/tex]


GET THE book : VECTOR ANALYSIS and an introduction to TENSOR ANALYSIS by

MURRAY R. SPIEGEL in SCHAUM'S OUTLINE SERIES

IT is very good in this kind of vector identities
 

FAQ: Vector Identities: Calculate \nabla \cdot (f \nabla \times (f F))

1. What is a vector identity?

A vector identity is a mathematical relationship or equation involving vectors. These identities are used in vector calculus to simplify and solve problems involving vector quantities.

2. What does the notation \nabla represent in the given vector identity?

The notation \nabla, also known as the del operator, is a vector differential operator in three-dimensional space. It is used to represent the gradient, divergence, and curl of a vector function.

3. How do I interpret the expression \nabla \cdot (f \nabla \times (f F))?

This expression represents the divergence of a vector field that is the result of taking the cross product of two vector fields, f and F, and then multiplying it by the scalar field f. The del operator \nabla is applied to this resulting vector field.

4. What is the significance of calculating \nabla \cdot (f \nabla \times (f F))?

Calculating \nabla \cdot (f \nabla \times (f F)) allows us to determine the behavior and properties of a given vector field. It can help us understand the flow and circulation of the vector field, as well as the presence or absence of sources or sinks.

5. Are there any practical applications of the vector identity \nabla \cdot (f \nabla \times (f F))?

Yes, this vector identity has various applications in physics, engineering, and other fields. For example, it can be used in fluid dynamics to analyze the flow of a fluid through a given region, or in electromagnetism to understand the behavior of electric and magnetic fields.

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