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Say I have my main "screen" plane, where vectors can be represented

enter image description here

I "know"/can represent vector Q, but the only information I know about vector R is relative to Vector Q. An easy way to visualize this is to have another plane at o2-- I can represent vector R in this plane (e.g. in cartesian coordinate form, or polar form), but how do I "globalize" to the original plane, or represent vector P?

Thank you

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2 Answers 2

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You first need to define the origin which everything is relative to. You've defined the origin (0,0) to be the top left corner of the main screen, and lets say that X goes positive to the left and Y goes positive downward.

To represent a vector, you need two pieces of information: 1) the location of the start and 2) the location of the end.

The location of the start is generally represented by a point (x,y) relative the coordinate system origin.

The location of the end can be represented by either another point relative to the coordinate system origin, or by a point relative to the starting point of the vector. Doesn't really matter as long as you do the math correctly whenever you use the vectors.

So for Q, it might be represented as start=(0,0) and end=(5,5). Since it starts at the origin, its "end" representation is the same regardless of whether your are making it relative to the origin or relative to the starting point of Q.

For P, lets say its start=(0,0) and end=(5,4).

For R, We can represent it either as start=(5,4) and end=(5,5) or we can represent it as start=(5,4) and end=(0,1), depending on whether the end point is relative to the origin or the starting point. It doesn't matter as long as you treat all vectors the same way.

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enter image description here

There are 2 types of vectors: position vectors and free vectors

You usually use position vectors in comouter applications, because they can very clearly represent a location (obviously). They also have a start point and an end point as every other vector, but their start position is in the origin (usually (0; 0)). In the image OA is a position vector.

Free vectors are have a start point that doesn't lie on the origin. This makes them excellent for pointing between 2 object or represent physical forces. On the image BC vector is an example for a free vector.

You can represent a free vector with 2 points. Because vectors are independent of their location, they can be freely moved around, and you get the same vector. Moving BC vector to the origin to create a position vector can be done by subtracting B from C, this the vector's length is |B - C|

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  • \$\begingroup\$ There are not different types of vectors, its how you apply them. Every vector "starts" at the origin point, but you can move that by applying another vector. So in your example you have a vector OB (from (0,0) to B). So you get to Point C by doing this: OB + BC = OC (vector from (0,0) to Point C). In another frame of reference, your origin may already be moved, so in this new frame of reference (FoR) your point C would be somewhere else in regards to the old FoR, but correct in the new FoR. Just dont tell someone, that there are two different kind of vectors. People may misunderstand that. \$\endgroup\$
    – PSquall
    Aug 14, 2018 at 10:19

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