What's the Difference Between a Position and a Position Vector?

In summary, a position vector is a vector in Euclidean space that points from the origin to a specific location, while position is a concept that can be described without relying on numbers in a Euclidean space. The main difference is that a position vector assumes the use of numbers, while position may not.
  • #1
san203
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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?
 
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  • #2
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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  • #3
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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  • #4
san203 said:
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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  • #5
phinds said:
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.

mathman said:
Position in a plane: (x,y)
Position vector in a plane: vector from (0,0) to (x,y)
But isn't position in plane also calculated relative to origin?

jbunniii said:
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.

Edit#2 : Thanks. Your answers were right i guess.
 
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  • #6
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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  • #7
HallsofIvy said:
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.
 
  • #8
A position vector is a vector in Euclidean space that points from the origin to your location
 
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  • #9
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.
 

1. What is the difference between position and position vector?

Position refers to the location of an object in space, typically described using a coordinate system. A position vector, on the other hand, is a mathematical representation of this position, consisting of a magnitude and direction. It is often used in physics and engineering to describe the position of an object relative to a reference point or origin.

2. How is position vector represented mathematically?

A position vector is typically represented using a tuple or array of numbers, with each number representing the magnitude of the vector in a specific direction. For example, in a 3-dimensional coordinate system, a position vector may be represented as (x,y,z), where x, y, and z are the components of the vector in the x, y, and z directions respectively.

3. Can a position vector have a negative magnitude?

Yes, a position vector can have a negative magnitude. This indicates that the object is located in the opposite direction of the vector. For example, a position vector of (-5,0) would represent an object located 5 units to the left of the reference point in a 2-dimensional coordinate system.

4. How is the position of an object determined using a position vector?

The position of an object can be determined by adding the position vector to the coordinates of the reference point or origin. This is known as vector addition. For example, if an object has a position vector of (3,2) and the reference point is at (0,0), then the object's position would be (3,2) + (0,0) = (3,2).

5. What is the relationship between displacement and position vector?

Displacement and position vector both describe the location of an object in space. However, displacement is a vector that describes the change in position of an object from its initial position to its final position. This means that displacement can be calculated using two position vectors, while a position vector only describes the position of an object at a specific point in time.

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