I"ve just started looking at the axioms of 3D Geometry. The first one that I encountered is this one:

"Three non collinear points define a plane" or " Given three non collinear points, only one plane goes through them"

I know that it is an axiom and it is taken to be true but I don"t understand the intuition behind it. I understand that if I take one point or any number of collinear points, then I can draw infinite planes just by rotating around the line that connects these points, but why do we need 3 non collinear points to define a plane, why not more? And why, given three non collinear points, does only one plane go through them? Why not two or three?


*

Two points determine a line (shown in the center). There are infinitely many infinite planes that contain that line. Only one plane passes through a point not collinear with the original two points:

*


*

Two points determine a line $l$. Thus, as you say, you can draw infinitely many planes containing these points just by rotating the line containing the two points. So you find a set of infinitely many planes containing a common line. For any third point not on $l$ then there is only one of these planes containing it.

You are watching: Two dimensional using 3 noncollinear points

An analogy is the same problem is lower dimension. Take a point in a plane. There are infinitely many lines through it. Now take a second point different from the first. Then there is a unique line among the infinitely many given that contains the two points.


*

A plane is a vectorial space whose dimension is $ 2$.its base contains exactly two independent vectors.If your three points $ A,B,C $ do not lie in the same line, you can take as a base, the couple $ (vecAB,vecAC) $.


*

Thanks for contributing an answer to les-grizzlys-catalans.orgematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Use les-grizzlys-catalans.orgJax to format equations. les-grizzlys-catalans.orgJax reference.

See more: State Agency Regulations Take Precedence Over Conflicting Federal Agency Regulations.

To learn more, see our tips on writing great answers.


Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy


Not the answer you're looking for? Browse other questions tagged geometry euclidean-geometry 3d or ask your own question.


Would I be correct to assume that the minimum amount of vertices required to have an object with 3 dimensions is 4?
*

site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.11.19.40795


Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.