You can calculate the deltas using trig, as long as you have the angle from one of the unit vectors ( in 2D ) and it''s magnetude.
That example of a rigid body is a bit misleading, because everything to do with that force, is in the vector. How the body reacts needs to take into account the point of impact of the force, but then that needs to take distance into account, which isn''t apart of vector spaces either. The actual force it''self doesn''t need to know anything about the body, at all.
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Difference between a point and vector
A point is a special type of vector. It''s a position vector (actually an application of the vector concept - not necessarily a physical point but a location in n-space). I think a vector is just an abstraction for any multidimensional value. In physics it''s usually defined in polar form but it can also be an ordered pair/triple/n-tuple.
Pyhon_regious: Force doesnt act in some abstract vector space.
It acts in real physical space. To have an unique solution you have to specify point of application. In physics, vector quantities are defined as objects with four properties:
-length (magnitude)
-direction
-orientation (vectors with same direction can be pararel or antipararel)
-point of application.
Those properties give an unique vector description.
Marshall: Points and vectors are different geometrical objects.
You can dacribe point as vector of length zero but you do not define in this way. Mathematical point has no definition, it is a basic concept like set. The geometrical definition of vector says that it is an ordered pair of points regardless of coordinate system you use. Sometimes it is better to use polar (cylindrical) coordinates and sometimes not, depending on ones problem.
K.
It acts in real physical space. To have an unique solution you have to specify point of application. In physics, vector quantities are defined as objects with four properties:
-length (magnitude)
-direction
-orientation (vectors with same direction can be pararel or antipararel)
-point of application.
Those properties give an unique vector description.
Marshall: Points and vectors are different geometrical objects.
You can dacribe point as vector of length zero but you do not define in this way. Mathematical point has no definition, it is a basic concept like set. The geometrical definition of vector says that it is an ordered pair of points regardless of coordinate system you use. Sometimes it is better to use polar (cylindrical) coordinates and sometimes not, depending on ones problem.
K.
Yeah. Since we cannot convince each other, we should leave this topic. So, till next thread 
K.
K.
Just in case all that confused you, Mindwarp, maybe this will clarify things:
A beachball is sitting somewhere at sea level. It will represent 0, 0, 0 in space. A car is somewhere else, 1028 feet east of the ball, 736 feet north of the ball, and 100 feet above sea level. The point of the car is therefore {1028, 738, 100). Now, that car is also moving. And, if you were to check on its position each minute, it would always be twenty feet north of where it had been the previous minute, thirty feet west of where it had been, and ten feet higher than it had been. It's movement vector, therefore, is {-30, 20, 10}. That's its movement vector regardless of where it is, as long as it's moving at the same speed and in the same direction. The magnitude of the vector - in this case the speed the car is moving at - is sqrt(-302 + 202 + 102). You'll probably notice that that is simply the distance equation, where one of the points is 0.
A vector simply represents a direction and a magnitude. It is often used to represent direction of movement and speed of movement. But it could also be used to represent the direction a beam of light is traveling in and it's brightness, or anything like that.
So a point is a dot somewhere in space. And a vector is an arrow with no location; just a length (or magnitude) and a direction it points in.
There's also an article here on Gamedev.net about the "World of Vectors and Planes" that should help you out.
Edited by - TerranFury on September 9, 2001 7:07:03 PM
A beachball is sitting somewhere at sea level. It will represent 0, 0, 0 in space. A car is somewhere else, 1028 feet east of the ball, 736 feet north of the ball, and 100 feet above sea level. The point of the car is therefore {1028, 738, 100). Now, that car is also moving. And, if you were to check on its position each minute, it would always be twenty feet north of where it had been the previous minute, thirty feet west of where it had been, and ten feet higher than it had been. It's movement vector, therefore, is {-30, 20, 10}. That's its movement vector regardless of where it is, as long as it's moving at the same speed and in the same direction. The magnitude of the vector - in this case the speed the car is moving at - is sqrt(-302 + 202 + 102). You'll probably notice that that is simply the distance equation, where one of the points is 0.
A vector simply represents a direction and a magnitude. It is often used to represent direction of movement and speed of movement. But it could also be used to represent the direction a beam of light is traveling in and it's brightness, or anything like that.
So a point is a dot somewhere in space. And a vector is an arrow with no location; just a length (or magnitude) and a direction it points in.
There's also an article here on Gamedev.net about the "World of Vectors and Planes" that should help you out.
Edited by - TerranFury on September 9, 2001 7:07:03 PM
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