How to express vector in sigma notation

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A vector A, can be expressed in sigma notation as
[tex]\sum[/tex] Ai where i runs from 1 to 3, i.e. A1 for x coordinate, A2 for y coordinate and A3 for z coordinate.

I wonder how to express vector A in polar form using sigma notation. Could anyone share their knowledge to me?
 

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  • #2
tiny-tim
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Welcome to PF!

Hi reckon ! Welcome to PF! :smile:

(have a sigma: ∑ :wink:)
A vector A, can be expressed in sigma notation as
[tex]\sum[/tex] Ai where i runs from 1 to 3, i.e. A1 for x coordinate, A2 for y coordinate and A3 for z coordinate.
No, it's ∑ Aiei, where the {ei} are basis vectors.
I wonder how to express vector A in polar form using sigma notation. Could anyone share their knowledge to me?
You'd need to use the basis vectors er eθ and eφ.

But these are different at each point, and at the origin they aren't even defined.
 
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Hahaha.. thx tiny-tim for ∑ and you even provided with "for copying-pasting" in your signature.

But I'm still a bit unsure because for eθ eφ, we only have angle which doesn't have dimension, isn't it? Can we make them as component of a vector?

A=rer + θeθ + φeφ
where r have length dimension while θ and φ have no dimension?
 
  • #4
tiny-tim
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Hi reckon! :smile:
But I'm still a bit unsure because for eθ eφ, we only have angle which doesn't have dimension, isn't it? Can we make them as component of a vector?

A=rer + θeθ + φeφ
where r have length dimension while θ and φ have no dimension?
ah … you obviously haven't come across these before …

no, er eθ and eφ are all unit vectors (with magnitude one), in the directions of increasing r, increasing θ, and increasing φ, respectively …

so they all have length dimension.

(it is traditional to use the symbol e for unit vectors)

A vector starting at the position (r,θ,φ) will be written as aer + beθ + ceφ, and a b and c have nothing to do with (r,θ,φ), they are simply the components of the vector in each of the three (perpendicular) directions. :smile:

(this would be easier to follow with a diagram, but unfortunately, I can't find a good one, in wikipedia or anywhere else :redface:)
 

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