Converting Radians to Vector Notation for Simplifying Expressions

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The discussion focuses on converting the arc length formula dL = R d@ into vector notation for simplification. Participants suggest using cylindrical or spherical coordinates to achieve this conversion, as these systems have established formulas that can aid in the process. There is a clarification about the distinction between vector and Cartesian coordinates, emphasizing the need for more context to provide accurate guidance. The importance of breaking down components is highlighted, as the arc length is initially a scalar quantity. Overall, further details or the complete problem statement are necessary for a more precise solution.
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The arc length of a circle is radius times the angle between the two radius legs that connect the arc. Thus
dL = R d@

and dF = I dL x B where B and dL and dF are vectors.

how can I convert dL = R d@ into vector notation so that I can simplify these two expressions??
 
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seems an odd question, and further ellaboration is needed.

By the sounds of it, maybe you should just use cylindrical r or spherical co-ordinates.

You should google cylindrical co-odinates. There are standard formulas and fudge factors involved, that will get you to your "vector" co-ordinates.

When you say "Vector" do you mean Cartesian co-ordinates?

If this is in relation to a homework problem, please post the whole question
 
(Don't know if you've gotten it since, but...) As far as I'm aware, s = \thetaR, where s is the arc length, \theta is the angle, and R is the radius, is entirely scalar. I can only see it "becoming a vector," if that makes sense, if you break literally everything up into components.

Could you please post the whole question?
 

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