# Determine whether a set of points lie on the same plane

All below

## Relevant Equations:

All below

AB, AB, AD are Ld, that is, the three vectors lie on the same plane, so, "yes, the points lie on the same plane"
However,
AB CB and AD are Li, that is, the three vectors span the space R3, and dont lie in the same plane, so, how can four points that lie on the same plane, that can generate only vectors that lie on the plane, generate a space?

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anuttarasammyak
Gold Member
Any three points, say A,B and C, are on the same plane, say P. Is the fourth one, D, is also on the plane P?
If the vectors satisfy the conditions you mentioned, yes it is.

LCSphysicist
Any three points, say A,B and C, are on the same plane, say P. Is the fourth one, D, is also on the plane P?
If the vectors satisfy the conditions you mentioned, yes it is.

But if A B C D are coplanar, AB CB and AD would need to lie in the plane too!