Given two lines joining A,B and C, D in 3D how do I figure out if they intersect, where they intersect and the ratio along AB at which the intersection happens? I can quite hapilly work out the equation for the lines in different forms. I'm guessing that you need to change them to parametric form, equate the equations and do some algebra ...

Find a line parallel to two planes and intersecting two lines. 0. Vectors and directed line segments. 3.

And you only need to prove the existence of two intersecting lines. That means: Choose any two points, draw the line through the line segment determined by those two points, and then draw a third point not on the first line. The only line through that third point that won't intersect the first line would be a line parallel to the first line.

Given coordinates of two lines which intersect when one line is extended, how to find their intersection coordinates? 1 Finding the angle between two lines meeting at one point.

The point $(1,-1,5)$ obviously satisfies the first equation, and the lines aren’t parallel, so if you’re not getting that as the point of intersection you’re making a mistake somewhere along the way.

In the examples given, the lines are defined by two points, but a direction vector may be obtained by taking the difference in the coordinates of the two given points. Here is the construction. We leave the proof as an exercise, so that the interested reader may benefit by working it out (hint: the Law of Sines is helpful).

2018年11月22日 · The most obvious approach would be to intersect the line with all six planes containing the cube's faces. This requires me to solve six 3×3 systems of linear equations which will probably take a while.

$\begingroup$ @bd1251252 The two lines intersect when they have the same values.

2020年8月26日 · $\begingroup$ if these two lines are intersect they have a intersection point that point lies on both lines so you can get that point as $<a,b,c>$ then tried to get system of equation and solve it $\endgroup$

This matrix equation is also equivalent to saying that the right hand side (which represents a vector from a point on one line to a point on the other line) is a linear combination of the direction vectors of the lines. It is a worthwhile exercise to see that this condition is equivalent to the two lines intersecting.