Determine whether a set of points lie on the same plane

  • Thread starter Thread starter LCSphysicist
  • Start date Start date
  • Tags Tags
    Plane Points Set
Click For Summary

Homework Help Overview

The discussion revolves around determining whether a set of points lies on the same plane, specifically examining the relationships between vectors formed by these points. The subject area includes vector geometry and linear dependence.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the conditions under which points are coplanar, questioning the implications of linear dependence and independence of the vectors formed by these points. There is discussion about the contradiction arising from the relationships between different sets of vectors.

Discussion Status

The discussion is active, with participants raising questions about the conditions for coplanarity and examining potential contradictions in their reasoning. Some guidance has been offered regarding vector relationships, but no consensus has been reached.

Contextual Notes

There are indications of potential errors in calculations, such as a sign error in a vector, which may affect the outcome of the discussion. Participants are also considering the implications of linear dependence among the vectors involved.

LCSphysicist
Messages
644
Reaction score
163
Homework Statement
All below
Relevant Equations
All below
1594693398811.png

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 don't 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?
 

Attachments

  • 1594693228803.png
    1594693228803.png
    4.7 KB · Views: 267
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: LCSphysicist
anuttarasammyak said:
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.
AB AD AC are LD, but AB CB and AD not!

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

It are contradictory, no?
 
In the solution, there's a sign error in ##\vec b##. Once you fix that, the determinant ends up not vanishing.
 
  • Like
  • Informative
Likes   Reactions: epenguin, anuttarasammyak and LCSphysicist

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
1
Views
2K
Replies
6
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 20 ·
Replies
20
Views
3K