Difference between Position Vector & Displacement Vector? (no calculatins)

[LearninDaMath]

Difference between "Position Vector" & "Displacement Vector?" (no calculatins..)

http://en.wikipedia.org/wiki/Position_(vector )

http://en.wikipedia.org/wiki/Displacement_(vector )


Is the position vector simply an initial vector given by coordinates (x,y) or (x,y,z) such as (8,4) or (8,4,5)..

While the displacement vector is simply the difference between two given vectors on an xy or xyz plane, such as Vector A minus Vector B representing ($\stackrel{9}{5}$) - ($\stackrel{5}{10}$) minus Vector C, being ($\stackrel{4}{-5}$) ..with Vector C being the Displacement Vector?


P.S. The numbers in the second paragraph are supposed to be vector columns. I tried to create them using the "stack" function under "above and below" in the Latex Reference menu.

 

[clesling]

A vector has a magnitude and direction. A position has no direction, but only occupys space. A displacement vector is in fact the difference between points in space occupying more than a single point with a magnitude and direction.

 

[I like Serena]

Yep.
Note that a position vector is also a displacement vector relative to an arbitrary origin.


In latex you can write vectors like

\begin{pmatrix} x \\ y \end{pmatrix}

which looks like:
$$\begin{pmatrix} x \\ y \end{pmatrix}$$

Some people prefer:
$$\begin{bmatrix} x \\ y \end{bmatrix}$$

 

[LearninDaMath]

Thanks, I like Serena, for the confirmation and the Latex notation help. Much appreciated!.

clesling, I think there is some confusion between "position" and "position vector." One is a point in space with no magnitude or direction and the other is a displacement between a point in space and an arbitrary origin. I am now confident that is correct :)

 

[asteriatic]

I don't know how to make them look like vectors.

Yes, you are correct. The position vector represents the location of a point in space with respect to a chosen origin. It is given by a set of coordinates, such as (x,y) or (x,y,z) in a Cartesian coordinate system. It is used to describe the position of an object in space.

On the other hand, the displacement vector represents the change in position of an object. It is the difference between the final position vector and the initial position vector. It is independent of the chosen origin and only depends on the final and initial positions of the object. It is used to describe the movement of an object in space.

In summary, the position vector is a fixed vector that describes the location of an object, while the displacement vector is a variable vector that describes the change in position of an object.