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

"Three non upright points specify a plane" or " offered three non collinear points, just one airplane goes with them"

I understand that that is one axiom and also it is taken to be true however I don"t recognize the intuition behind it. I recognize that if i take one allude or any number of collinear points, then ns can draw infinite planes just by rotating approximately the line the connects these points, however why execute we require 3 non upright points to define a plane, why not more? and also why, offered three non upright points, does just one plane go through them? Why not two or three?


Two points recognize a heat (shown in the center). There space infinitely many infinite planes that contain that line. Only one airplane passes v a point not collinear v the initial two points:



Two points recognize a line $l$. Thus, together you say, friend can attract infinitely many planes containing this points simply by rotating the line containing the 2 points. For this reason you discover a set of infinitely numerous planes containing a typical line. Because that any third point no on $l$ then there is only one of these airplane containing it.

You are watching: How many noncollinear points are needed to define a plane

An analogy is the same trouble is lower dimension. Take it a allude in a plane. There space infinitely many lines v it. Currently take a second point various from the first. Then there is a distinct line among the infinitely countless given that contains the two points.


A aircraft is a vectorial room whose measurement is $ 2$.its base consists of exactly 2 independent vectors.If your three points $ A,B,C $ do not lied in the same line, you can take together a base, the pair $ (vecAB,vecAC) $.


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