# Kinematics Problem

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colossal    633
I'm having a hard time wrapping this problem around my head. Right now I have 2 Vectors in 3D space, and with each a distance float that represents the length of a line segment that starts from their respective Vector position. How do I determine the position where these line segment endpoints meet in 3D space ( to form almost like a joint if you will) ? Especially if there is technically more than one solution to the problem?

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Adding the velocity/vector to your starting points will give you your ending points, so you can just compare the ending points to see if they would end up at the same position. Here's an example:
Say you have 2 2D Points a, b where a = (2, 3) and b = (0, 0).
The 2 points each have a 2D velocity vector A, B respectively where A = <9, 7> and B = <12, 9>.
The end points for a and b are a' and b' respectively, and we calculated them like so:
a' = a + A = (2, 3) + <9, 7> = (2 + 9, 3 + 7) = (11, 10)
b' = b + B = (-1, 1) + <12 , 9> = (-1 + 12, 1 + 9) = (11, 10)
So a' is now at (11, 10) and b' is also at (11, 10).
My example is in 2D, but making the switch to 3D should be trivial.

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Paul65    126
Not sure I exactly understand the problem, but sounds like what you are saying is that you have two positions in space and from each extends a rod whose length is fixed. You want to rotate these rods so that they meet at their end points. If this is right, then if you think about it, they can meet on any point on a circle that lies directly between the two points. One important thing to remember though is that if the rods are too short, the rods cant meet at all, so they'll be no solution.

[quote name='colossal' timestamp='1306274161' post='4815326']
I'm having a hard time wrapping this problem around my head. Right now I have 2 Vectors in 3D space, and with each a distance float that represents the length of a line segment that starts from their respective Vector position. How do I determine the position where these line segment endpoints meet in 3D space ( to form almost like a joint if you will) ? Especially if there is technically more than one solution to the problem?
[/quote]

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I thought at first he was asking how to tell if two vectors will meet at the same location. I guess he is asking if two vectors intersect. That is a slightly more complicated question that I didn't know off of the top of my head so I googled it. But it is late and I wasn't finding anything that looked familiar from Calculus, but there are a few sites out there with how to calculate this. Sorry for the incorrect answer before.

As far as the number of solutions, this will have three types of solutions; no solution if the two vectors do not meet, a single solution at the point where the two vectors meet, or infinite solutions if the two vectors are starting at the same point and traveling in the same direction.