# Further maths vectors. Proving 2 lines lie in the same plane

How do I show that the following 2 lines lie in the same plane.
L1: r = i - j + 4k + t(2i - j + 3k)
L2: r = i + 3k + s(i- j + 2k)
(edited 6 months ago)
Original post by Amy.fallowfield
How do I show that the following 2 lines lie in the same plane.
L1: r = i - j + 4k + t(2i - j + 3k)
L2: r = i + 3k + s(i- j + 2k)

You have two points on the plane and two directions. A plane can be defined by a point on the plane and 2 directions. So form the plane and show the other point satisfies it (or similar).
Original post by mqb2766
You have two points on the plane and two directions. A plane can be defined by a point on the plane and 2 directions. So form the plane and show the other point satisfies it (or similar).

Ah ok thank you
Original post by Amy.fallowfield
Ah ok thank you

I think it should also be sufficient to show that the two lines intersect.
Check the possibility that the lines are parallel and different. In which case, you can three points.

If not parallel,

either show lines intersect, which means you can have three or more points on the plane formed by two lines. as a safe approach, show that you can normal to the plane.

another approach is to show that lines are not skew.