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# distance between vectors

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I haven''t done alot of maths lately which has made me fogot alot of things. However what I want to know is how to get the distance between vector and vector in 3D space. The idea I have looks something like this: |v3| = |(v2-v1)| Heh, I''m not good at writing math formulas, but hey it makes me look smarter So if you don''t understand it then: v3 = v2-v1; v3.length = sqrt(v3.x*v3.x+v3.y+v3.y+v3.z+v3.z); Is this correct?

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Distance between two vectors? Vectors are not fixed in space; they have magnitude and direction, but not position, so the concept of "distance" doesn''t seem to make much sense.

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I think he/she meant vertex.

[edited by - Newfound Ajarn on November 11, 2003 11:42:02 PM]

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correct, vectors do not have position so you can't have a distance between them. if you are talking about specific vectors anchored at specific points, then you just need to find the distance between the two points which is:

v = vector between 2 points
v = (p1.x - p2.x, p1.y - p2.y, p1.z - p2.z);
distance between the points = |v| = sqrt(v.x^2 + v.y^2 + v.z^2);

-me

[edited by - Palidine on November 11, 2003 11:46:39 PM]

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You accidentally put "+" instead of "*" between the Y and the Z terms. Fix that, and you''ve got it.

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quote:

Distance between two vectors? Vectors are not fixed in space; they have magnitude and direction, but not position, so the concept of "distance" doesn't seem to make much sense.

I knew this would come up, and I thought about editing my post but I thought; "na, they can't be that priggish", well I was wrong.

quote:

You accidentally put "+" instead of "*" between the Y and the Z terms. Fix that, and you've got it.

typo

[edited by - angry on November 11, 2003 12:06:44 AM]

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Just for reference: Angel (Interactive Computer Graphics et al.) describes the difference between what you call a vector and a point as a true-vector and a position-vector.

A vector is simply a mathematical data structure - some people choose to think of it that way whilst others choose to think of it in more semantic terms: point and vector (where vector denotes a direction with magnitude). The fact is, if you regard a vector simply as a data structure then a vector can represent a position with respect to the origin in any 3D space.

Quite clearly, there are 2 schools of thought on this...

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Vectors do not even have to contain numbers! Vector spaces can be taken over lots of different fields.

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Just curious how you would define distance? Personally I would call distance a measure of how close two values are to one another. Also if a point is a position vector then how can there be a distance between points, but not vectors since a point is a vector.

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A point can be represented by a vector, but not the other way around. Distance can be defined in many ways ( in maths we call then metrics ), any distance or metric function must fulfil...

1) d(x,y) = 0 iff x = y
2) d(x,y) = d(y,x) for all x,y in the space
3) d(x,y) <= d(x,z) + d(z,y) for all x,y,z in the space

The Euclidean distance we most commonly use for vectors in an example of this

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