Proving Vector Identity in Cartesian Coordinates

In summary, a vector identity is a mathematical equation that describes the relationship between two or more vectors. To prove a vector identity, basic vector operations and algebraic techniques are used. These identities are important in simplifying and solving complex vector equations and have applications in various fields. Vector identities can be derived from each other and are not limited to 3-dimensional space.
  • #1
QuantumDefect
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Hello, I need some help on this vector identity. I am supposed to prove that Del Dot (Del(g(r)))=(2/r){dg(r)/dr}+(d^2g(r)/dr^2). Using Cartesian Coordinates. Any help would be GREATLY appreciated> :)
 
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  • #2
How is r related to your Cartesian coordinates?
Do you know the chain rule?
 
  • #3
r^2=x^2+...?


I think that's what I have to do! I was using r=x*x_hat+... Ill try that, thanks!
 

1. What is a vector identity?

A vector identity is a mathematical equation that describes a relationship between two or more vectors. It is used to prove the equality of vector expressions and is a fundamental concept in vector calculus.

2. How do you prove a vector identity?

To prove a vector identity, you must manipulate the given vectors using basic vector operations such as addition, subtraction, and scalar multiplication. You may also use algebraic techniques and trigonometric identities to simplify the expressions and show that they are equal.

3. What is the importance of vector identities?

Vector identities are important because they allow us to simplify and solve complex vector equations. They also provide a basis for understanding and solving problems in physics, engineering, and other fields that involve vector quantities.

4. Can vector identities be derived from each other?

Yes, vector identities can be derived from each other by using the rules of vector algebra and trigonometric identities. This process is known as vector identity manipulation and is used to prove more complex vector equations.

5. Are there any common misconceptions about vector identities?

One common misconception about vector identities is that they only apply to 3-dimensional space. In reality, vector identities can be used in any number of dimensions and are not limited to 3-dimensional problems.

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