Dot products in spherical or cylindrical coordinates

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Homework Help Overview

The discussion revolves around calculating the dot product of two vectors in spherical coordinates, specifically when both vectors possess only an r component. The original poster seeks clarification on whether it is sufficient to multiply the r components directly.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants suggest visualizing the vectors to determine if they are parallel and question the implications of the dot product in this context. The original poster considers the relationship between the electric field and electric displacement vectors, noting their parallel nature.

Discussion Status

The conversation is ongoing, with participants exploring the conditions under which the dot product can be simplified. Some guidance has been offered regarding the importance of checking vector orientation and definitions, but no consensus has been reached on the specific calculation method.

Contextual Notes

The original poster has indicated that both vectors are defined in spherical coordinates and possess only an r component, which may influence the discussion on the dot product.

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Homework Statement


I'm doing a question that requires me to take the dot product of 2 vectors in spherical coordinates. Both vectors have only an r component, can I just multiply the r components?

Homework Equations

The Attempt at a Solution

 
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Sketch the vectors and see.
Do they both point in the same direction?
What does a dot product do?
 
Sorry probably should have been more specific. The 2 vectors are actually an electric field and electric displacement. Both have only an r component. Based on what you have said I assume that if they are parallel you can just multiply the components together. Since both the electric field and displacement have only an r component I assume that they are parrallel at all points and thus the dot product is equal to the product of the r components. Does this make sense?
 
You can check by sketching the vectors and looking... are they parallel? You should be able to see.
The next question is if the dot product of parallel vectors is just the product of their magnitudes... you should not have to assume anything here: check the definition of dot product and you will know.
 

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