I have the following problem, which Google has not yet been able to answer.
I have the equations to two lines in 3D space. I also have the co-ordinates of a single point on each line. I can therefore find the co-ordinates of a third point on either line and compute the equation to a plane that contains both lines.
Now what I need to do is to compute the equation to the normal lines to each of these lines so that both normal lines are also on this plane. After this, I need to find the point of intersection of these two lines.
I'd appreciate any help on this topic.
PS: This is my first post on MSE, so if I'm violating any MSE rules, please point them out so that I can correct my post and not make such a mistake in the future
EDIT More information as requested in the comments:
I'm not trying to solve a specific question. I'm trying to write a program that is flexible enough to do this.
So as parameters to this program, I have values for A, B, C - the coefficients for the equations to the lines written as Ax + By + C = z.
I know that for every pair of lines, there is a plane on which these two lines reside. I will therefore need to compute the equation to this plane.
The idea is that there is an object moving along a path (some curve) on a plane (some plane whose equation I must compute), that I detect with a sensor. I am allowed to assume a monotonous curve between any two consecutive detections. I need to figure out the coordinates of the center of the circle on whose circumference this monotonous curve exists.
Please let me know if that clarifies the question