Does vectors have a position at all? If I have understood it right a normal vecotor doesn't unless it is a free vector (zero vector). Am I on the right track here?
Last edited by NoteMe; Nov 30th, 2004 at 11:22 PM.
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Vectors don't really have a position, they are used to describe a position (relative to something, possibly the origin) or a direction.
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Yeah I know that vecotrs have a direction, and a length, and that is what I have used it for. But I have started some new tutorials (going to be DX tutorials, but first I want to explain some of the math) and in one of the books I am using for reference it says:
Vectors are not only used to define the position of vertices, they are also used to define a direction
And they are not explaining it any furuther. But the last section in front of it talked about free vectors/zero vectors. So maybe thats the only vectors that defines a point....not sure...never thought about them that way before.
It's very simple. A (position) vector, say (3,2,1) can be said to define a point at x=3,y=2,z=1 from the origin (0,0,0). There's nothing complex about it - you likely know all you need to.
Originally posted by azteched It's very simple. A (position) vector, say (3,2,1) can be said to define a point at x=3,y=2,z=1 from the origin (0,0,0). There's nothing complex about it - you likely know all you need to.
Yeah that is a free vector or a / zero vector. But if you have 2 points (and non of them is origo) and use subtraction to find the vector between those points. Can you still say that that vector has a position.
Posted by NoteMe Yeah that is a free vector or a / zero vector. But if you have 2 points (and non of them is origo) and use subtraction to find the vector between those points. Can you still say that that vector has a position.
Doing that will give you a position vector which will describe the direct one of those points is from the other one. This vector doesn't have a position but the point it is pointing to is merly for showing the relative position of the two vectors.
I'll do an example and a pic one sec....
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On here you see the Blue & Red Vectors describing positions.
If you then subtract them you get the green vector. Interperated as a position vector it gives you the green dot but if you use it as a direction vector then it describs the motion from Blue to red or from any position in that direction for that amount. So if you are thinking of it as a direction vector it doesn't really have a position associated with it just a direction . Hope that helped .
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Got a bit confused there.....but am I right if I say that you concluded with:
- Only free or zero vectors have a position (those who starts at origo), the rest only holds a direction and a length and are not bound to any position at all.
After all these years I always thought vectors only represent Direction and Magnitude. Vector's mathamatically don't have position (Remember that vector's aren't points.) Vectors are made by subtracting two points in 3D space. That means that a Vector always has a head (Point2) and a tail (Point1, which is the origin of the vector.)
Like for example, let's say Point1 is located at (10,0,0) and Point2 is located at (30,0,0). When you create a vector, you always subtract Point2 from Point1. So that would mean:
Calculating that, your vector is now (20,0,0) . To get the magnitude of it, you do this:
Sqr(V.X * V.X + V.Y * V.Y + V.Z * V.Z)
Using the value we have now, the magnitude is 20 (obviosly). Playing around with the Y and Z values would increase/decrese the magnitude.
Now saying that the vector is located at 20,0,0 wouldn't really make any sence mathamatically. It only represents Magnitude and Direction. The XYZ components of the vector were only needed to later be calculated for magnitude and direction.
Last edited by Jacob Roman; Nov 30th, 2004 at 11:13 PM.
I found the final answer right now......happy to clear this out.
A BOUND vecotr has these atributes:
A starting point
A final point
A direction
A magnitude
But a free vecotr isn't the same. You don't have a starting point when you are dealing with free vectors. So what is the diffrence on a poin and a free vector. A free vector is represented additionally by magnitude and direction. The magnitude of a vector (4, 4, 4) is the distance between the origin and the final point. If you only need the final point then it is a 3D point. If you need a magnitude and direction then it is a vector.
So now we know the truth...and I was right all the way from the start...
Posted by NoteMe Got a bit confused there.....but am I right if I say that you concluded with:
- Only free or zero vectors have a position (those who starts at origo), the rest only holds a direction and a length and are not bound to any position at all.
Sounds like what i was saying, think this is the same thing you've put in your next post just with more words .
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Vectors
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. Hope that helped 
