Dot products in spherical or cylindrical coordinates

[phys-student]

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

 

[Simon Bridge]

Sketch the vectors and see.
Do they both point in the same direction?
What does a dot product do?

 

[phys-student]

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?

 

[Simon Bridge]

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.