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I don't know why) an "arrow" even though it is not an arrow, with direction and magnitude. It happens to have the same coordinates, but it is fundamentally different from the previous one.The first thing I said is a "scalar", the second one is a "vector". When we need to distinguish between the two, we use arrows (or boldface, or other means of notation).In summary, position vectors are used to represent the location of a point in space, and are distinguished from scalars by the use of arrows or boldface notation. They have nothing to do with whether the point is stationary or moving, but rather represent a specific location in terms of unit vectors and coordinates.f

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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

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

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

Zz.

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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?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 anydirection! 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 aposition vector! Each of those locations are defined in terms of unit vectorsrandθ, oriandj.

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

Zz.

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I don't understand the point here in the context above 'Each of those locations are defined in terms of unit vectorsIf 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 anydirection! 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 aposition vector! Each of those locations are defined in terms of unit vectorsrandθ, oriandj.

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

Zz.

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

I don't understand the point here in the context above 'Each of those locations are defined in terms of unit vectorsrandθ, oriandj.' could you simplify it, please?

##\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.

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Mentor

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

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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.… position vectors are stationary, they do not have any displacement so why do they possesses arrows on the top of them?

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Science Advisor

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On the other hand, position vectors are stationary, they do not have any displacement

You probably don't mean that "position vectors are stationary" You mean that

.

"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)}##.

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Science Advisor

Gold Member

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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.)'

I don't understand the point here in the context above 'Each of those locations are defined in terms of unit vectorsrandθ, oriandj.' could you simplify it, please?

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Hi,

I am new to this forum but I wanted to share with a draft of a short paper that I wrote to clarify some issues I had with the understanding of a position vector.

My experience with the position vector was bad, especially when using cylindrical and spherical coordinates. I was not able to find a logical explanation why the position vectors in these coordinate systems were different than the position vector in Cartesian coordinates. The answer may be out there somewhere but I was not able to find it. I have performed an incomplete research in this topic and I think I finally got an answer.

I am attaching my first draft of the paper and be warned that I am not an expert in math - just a math fan. Still, there is some work to be done to complete it. For instance, I need to practice and do problems with general oriented vectors in the above mentioned coordinates. Anyway, I wanted to post it hoping that I can get some comments and find out if I am just wasting my time.

I thought this thread was a good starting point. Thank you for your help.

I am new to this forum but I wanted to share with a draft of a short paper that I wrote to clarify some issues I had with the understanding of a position vector.

My experience with the position vector was bad, especially when using cylindrical and spherical coordinates. I was not able to find a logical explanation why the position vectors in these coordinate systems were different than the position vector in Cartesian coordinates. The answer may be out there somewhere but I was not able to find it. I have performed an incomplete research in this topic and I think I finally got an answer.

I am attaching my first draft of the paper and be warned that I am not an expert in math - just a math fan. Still, there is some work to be done to complete it. For instance, I need to practice and do problems with general oriented vectors in the above mentioned coordinates. Anyway, I wanted to post it hoping that I can get some comments and find out if I am just wasting my time.

I thought this thread was a good starting point. Thank you for your help.

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