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How do you find the intersection of two 3d lines on a 3d plane?
Wiki User
∙ 13y ago
You need to more precise in your question. There is no guarantee two lines interection in 3-d space. If they do intersect, they must lie in the same plane. And that plane would only need to be 2-D, aside from the trivial case where the lines are the same.
If the two lines do intersect then x value for the two lines will be equal, as well as the y value & z value, in the equations of the two lines.
Using parametric equations, If line1 is given by: x = x1 + a*t, y = y1 + b*t, and z = z1 + c*t; and line 2 is: x = x2 + d*s, y = y2 + e*s, and z = z2 + f*s, where x1,y1,z1 & x2,y2,z2 are starting points [a,b,c] & [d,e,f] are direction vectors, and s & t are the parameters.
Since the x values must be equal, set x1+a*t = x2+d*s, and y1+b*t = y2+e*s, then you have two equations and two unknowns. Solve for t and s, then substitute into the z equations to find the z coordinate (they will both come up with the same z-value if indeed the lines do intersect). Even if both equations use 't' as the parameter, you need to treat them as two independent variables(so change one of them to s), since the lines could be changing differently as the parameter variable changes.
Wiki User
∙ 13y ago
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What is the name of an intersection of two nonparallel lines in a plane?
a point
If two parallel planes are cut by a third plane the lines of intersection are?
Parallel lines.
What is formed on a grid by the intersection of two number lines?
A coordinate plane.
If two parallel planes are intersected by a third plane the lines of intersection are parallel.?
Yes, they are.
Do two perpendicular lines intersect?
yes... In fact, any two lines on the same plane that are not parallel will share a point of intersection.
What does not have a point of intersection?
Two parallel lines, a plane and a line in a plane parallel to it.
What is the name of an intersection of two nonparallel lines in a plane?
a point
The plane formed by the intersection of two number lines?
Origin
If two parallel planes are cut by a third plane the lines of intersection are?
Parallel lines.
What is formed on a grid by the intersection of two number lines?
A coordinate plane.
What is the intersection of two perpendicular lines in the same plane?
A right angle.
Is the intersection of a line a point?
The intersection of two lines is always a point or the line itself. The intersection of a line with plane also the same as above.
If two parallel planes are intersected by a third plane the lines of intersection are parallel.?
Yes, they are.
Do two perpendicular lines intersect?
yes... In fact, any two lines on the same plane that are not parallel will share a point of intersection.
What are lines formed by the intersection of two number lines that meet at right angles at there zero points?
coordinate plane
What is the common point at which two lines meet?
point I believe the word you're looking for is "intersection". Two non-parallel lines that lie in the same plane will have one point in common where they cross, and that point is the intersection.
When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
