# Position and Position vector

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## Main Question or Discussion Point

What is a position vector? Is their any difference between the position vector and position? Isnt position of a point supposed to represent its direction in Cartesian plane as well(Positive quadrants , negative quadrants). So why two different terms?

phinds
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Just at a guess, I'd say it's like this: position in a 2D Cartesian coordinate system is absolute and is described by two numbers. A position vector is relative to some starting point, which MIGHT be the origin but might not be.

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jbunniii
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One might say that a position vector $[x\,\,y]$ is the equivalence class of pairs of points $(a,b)$, $(c,d)$ in the plane satisfying $c-a = x$ and $d-b = y$.

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mathman
What is a position vector? Is their any difference between the position vector and position? Isnt position of a point supposed to represent its direction in Cartesian plane as well(Positive quadrants , negative quadrants). So why two different terms?
Position in a plane: (x,y)
Position vector in a plane: vector from (0,0) to (x,y)

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Gold Member
Just at a guess, I'd say it's like this: position in a 2D Cartesian coordinate system is absolute and is described by two numbers. A position vector is relative to some starting point, which MIGHT be the origin but might not be.
Position in a plane: (x,y)
Position vector in a plane: vector from (0,0) to (x,y)
But isnt position in plane also calculated relative to origin?

One might say that a position vector $[x\,\,y]$ is the equivalence class of pairs of points $(a,b)$, $(c,d)$ in the plane satisfying $c-a = x$ and $d-b = y$.
Sorry. I didnt understand that at all.

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HallsofIvy
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Personally, I don't like the very concept of a "position vector"- it only makes sense in Euclidean space. When I was young and foolish (I'm not young any more) I worried a great deal about what a "position vector" looked like on a sphere. Did it "curve" around the surface of the sphere or did it go through the sphere? The answer, of course, is that the only true vectors are tangent vectors that lie in the tangent plane to the surface at each point.

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Gold Member
Personally, I don't like the very concept of a "position vector"- it only makes sense in Euclidean space. When I was young and foolish (I'm not young any more) I worried a great deal about what a "position vector" looked like on a sphere. Did it "curve" around the surface of the sphere or did it go through the sphere? The answer, of course, is that the only true vectors are tangent vectors that lie in the tangent plane to the surface at each point.
This really went over my head, but when i do learn things like this i'll try to keep what you said in mind.

A position vector is a vector in Euclidean space that points from the origin to your location

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I would say that the biggest difference is that a position vector assumes you are working in a space with numbers (like a Vector Space) and a position may not.

If you are studying Euclidean Geometry, based on the Elements, there are no numbers (at least for many books there is no need of numbers). So a position might be described as the intersection of two lines, or the center of a circle. In this case, there is no position vector, only a position. You are working in a Euclidean space that does not have the usual Vector Space information available.