# B Why do position vectors have an arrow on top of them?

1. Jul 20, 2018

### Indranil

According to the vector definition, the vectors have both the direction and magnitude such as displacement vectors which should possess arrows on the top of them because they have displacement so they express a direction. On the other hand, position vectors are stationary, they do not have any displacement so why do they possess arrows on the top of them? Could you explain, please?

2. Jul 20, 2018

### Staff: Mentor

They are the displacement of the origin of the coordinate system, resp. of the point $\{\,0\,\}$ in the vector space.

3. Jul 20, 2018

### ZapperZ

Staff Emeritus
If you ask me "where is the ball?", and I reply "Oh, it's 3 meters away", do you think you have sufficient information to locate the ball immediately?

No, because if it is 3 meters away from me, it could be 3 meters away in any direction! The only thing you can do is draw a circle of radius r = 3m, and the ball is someone on that circle.

If I say, it is 3 meters way in THAT direction (and I point), then you look at the direction that I'm pointing, and the intersection of that and the circle is the location of the particle. I've just given you the location in plane-polar coordinates. I could have easily given it to you in cartesian coordinates. And by doing that, I've defined a position vector! Each of those locations are defined in terms of unit vectors r and θ, or i and j.

It has nothing to do with whether something is stationary or moving.

Zz.

4. Jul 20, 2018

### Indranil

I understand a bit but not completely what you mean because English is not my first language and I am learning Physics here very easily. So I request you to use lucid language so that I can understand easily and clear my all concepts. So, please could you get your point a little bit easier here in this context above?

5. Jul 20, 2018

### Staff: Mentor

We represent all vectors with arrows over them to distinguish them from scalars. Another way of doing this is to represent vectors using boldface, rather than with arrows over them.

6. Jul 21, 2018

### Indranil

'
I don't understand the point here in the context above 'Each of those locations are defined in terms of unit vectors r and θ, or i and j.' could you simplify it, please?

7. Jul 21, 2018

### Staff: Mentor

$(a,b)$ is a position, a location with coordinates $a$ and $b$.

$\stackrel{\longrightarrow}{(a,b)}$ is a vector, sometimes called position vector. It is the vector starting at the origin $(0,0)$ and pointing to the location $(a,b)$. It has length and direction, which is why it is denoted as a vector. The fact that both are basically written as $(a,b)$ only means, that such a notation depends on the context, i.e. whether it stands for a point or for a vector. An arrow above it resolves this ambiguity.

8. Jul 21, 2018

### Staff: Mentor

To help distinguish them I favor writing vectors with coordinates using angle brackets -- <a, b>, and points using paretheses -- (a, b).

9. Aug 5, 2018

### David Lewis

Because that's the order in which the vector is read; from origin to head. The vector doesn't signify anything moving in the real world. In some cases the arrowhead has nothin to do with (or is in a different direction than) the motion. For example, a force on a static object, where there is no motion, or the direction of a moment or angular velocity vector.

10. Aug 5, 2018

### Stephen Tashi

You probably don't mean that "position vectors are stationary" You mean that an object that is stationary has a constant position vector. (Likewise, an object that has a constant velocity has a constant velocity vector.)
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"Displacement" is a word often used to suggest movement - something that would change as function of time. However, a "displacement" in the mathematics of vectors need not indicate an actual physical process. If an object has coordinates (3,2) we can imagine that the object arrived at (3,2) by making a journey from (0,0) even though it didn't really do that. That's a simple interpretation of what @fresh_42 is telling you about position vector $\overrightarrow{(3,2)}$.

11. Aug 7, 2018

### sophiecentaur

The displacement from me too you has a different sign from the displacement from you to me. Direction counts just as much for position as for velocity and all the other vectors. (Displacement is not distance.)