# Is the position vector a real vector?

• I
• WildBohr137
In summary, the position vector is a real vector, but it can change in magnitude and direction depending on the reference frame that is used.
WildBohr137
Is the position vector a real vector?
I have a hard time with this question because vectors are unchanged if I were to change my reference frame.
Example: If I place a pencil such that it points towards the door. It doesn’t matter what I define my origin to be. The pencil’s length and direction remain unchanged.
However this is not true for the position vector. Example: If I move my origin back 5 meters then the position vector changes its magnitude and direction.

Please let me know if I have been trolled here.

Indeed, position is better characterized as an affine space than a vector space.

A vector space has some operations that don’t make sense for the space of positions. Specifically, the addition of two positions doesn’t make sense (which position is the position of New York plus the position of Paris?), nor does the multiplication of a position by a real number (which position is 5 times the position of New York?).

However, the difference between two positions is a vector, and differences in position form a vector space with sensible addition and multiplication operations.

In curved spacetimes positions lose even their affine structure. In curved spacetime the best mathematical structure is a manifold. The difference between two positions is no longer a vector except locally.

David Lewis, phinds, sophiecentaur and 3 others
Dale said:
Indeed, position is better characterized as an affine space than a vector space.

A vector space has some operations that don’t make sense for the space of positions. Specifically, the addition of two positions doesn’t make sense (which position is the position of New York plus the position of Paris?), nor does the multiplication of a position by a real number (which position is 5 times the position of New York?).

However, the difference between two positions is a vector, and differences in position form a vector space with sensible addition and multiplication operations.

In curved spacetimes positions lose even their affine structure. In curved spacetime the best mathematical structure is a manifold. The difference between two positions is no longer a vector except locally.

WildBohr137 said:
"It's not for me, Doctor; it's for a friend.

But you were the one to go to the trouble of asking the question. 10/10

WildBohr137
sophiecentaur said:
"It's not for me, Doctor; it's for a friend.

But you were the one to go to the trouble of asking the question. 10/10
Haha thanks!

What is a real vector?

WildBohr137
malawi_glenn said:
What is a real vector?
It's not one of those knock-off fake vectors that you get from Southeast Asia

malawi_glenn
malawi_glenn said:
What is a real vector?
One that the is fully automatic:

haushofer said:
One that the is fully automatic:
Yoiks, that dog running downrange almost wasn't a real dog anymore...

sophiecentaur

## Is the position vector a real vector?

Yes, the position vector is considered a real vector in physics and mathematics. It originates from a fixed reference point, usually the origin, and points to a specific location in space, representing the position of a particle or object in a coordinate system.

## What distinguishes a position vector from other types of vectors?

The position vector specifically denotes the location of a point in space relative to an origin. Unlike other vectors that may represent quantities such as velocity or force, the position vector's primary role is to specify a point's coordinates in a given reference frame.

## Can a position vector change over time?

Yes, a position vector can change over time if the point it represents is moving. In such cases, the position vector will vary as the coordinates of the point change, reflecting its new location in space at different times.

## How is a position vector represented in a coordinate system?

A position vector is typically represented as an ordered pair or triplet of coordinates in a Cartesian coordinate system. For example, in three-dimensional space, the position vector r can be written as r = (x, y, z), where x, y, and z are the coordinates of the point in the x, y, and z directions, respectively.

## What are the applications of position vectors in real-world scenarios?

Position vectors are crucial in various fields such as physics, engineering, and computer graphics. They are used to describe the location of objects, navigate robotic movements, simulate physical systems, and render scenes in computer graphics by defining the positions of objects and cameras in a virtual space.

• Other Physics Topics
Replies
3
Views
3K
• Differential Geometry
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
1K
• Classical Physics
Replies
24
Views
2K
• Special and General Relativity
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
941
• Other Physics Topics
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
23
Views
646
• Other Physics Topics
Replies
26
Views
3K
• Quantum Physics
Replies
14
Views
1K