# Thread: [SOLVED] Determine if the following two lines intersect.

1. ## [SOLVED] Determine if the following two lines intersect.

Determine if the following two lines intersect. If they intersect, find the point of intersection. If they do not intersect, identify whether they are parallel, coincident or skew lines.

L1:
x = 1 + 2t
y = -1 - t
z = 3t

L2:
x = 1 + 3s
y = 2 + 2s
z = 3 + 4s

Im not sure how to start this question. I can manipulate the formulas just unsure of where to begin.
Thanks.

2. For two lines to intersect, don't they have to share a point? If so, then:

. . . . .1 + 2t = 1 + 3s
. . . . .-1 - t = 2 + 2s
. . . . .3t = 3 + 4s

Pick any two of the equations, and solve the resulting system of equations for the values of "s" and "t".

Whatever the result, plug that into the remaining original equation, and see if it works. If it does, then I believe you have an intersection point. Otherwise, not.

3. thank you very much for you quick reply.
I have done that and find out that they do not intersect, thus they will be either parallel or skew. And since their direction vectors are not collinear they are skew lines.
Thanks