How many noncollinear points make a plane

Figure 1. Line l is such that it passes through A, B and C. Hence points A B and C are collinear. In the case of points P, Q and R there can be no single line containing all three of them hence they are called non-linear.

Similarly points and lines which lie in the same plane are called coplanar otherwise they are called non-coplanar. Axiom : A plane containing a line and a point outside it or by using the definition of a line, a plane can be said to contain three non-collinear points. Conversely, through any three non collinear points there can be one and only one plane figure 1. Axiom : If two lines intersect, exactly one plane passes through both of them figure1.

Axiom : If two planes intersect their intersection is exactly one line figure 1. Introduction 1. Support the Monkey!

Tell All your Friends and Teachers. Get Paid To Take Surveys! Learn more. Why do three non collinears points define a plane? Ask Question. Asked 1 year, 4 months ago.

Active 1 year, 4 months ago. Viewed 2k times. 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.

Tom Avery Tom Avery 81 9 9 bronze badges. Another way to think about it is to connect those points by segments to get a triangle, and a triangle uniquely specifies the plane it is in. Yet another way to see it is to take one of the points as the origin, and form two vectors connecting it to the other two. Two non-collinear vectors span a plane. The three points are the origin and the tips of the two vectors, you wouldn't have two linearly independent vectors if the three points weren't non collinear.

Is this useful at all? Maybe you should clarify the reason why it doesn't convince you Add a comment. Active Oldest Votes. David G. Stork David G. Stork Gibbs Gibbs 7, 4 4 gold badges 12 12 silver badges 28 28 bronze badges. I prefer to give an analogy in low dimension than introducing rigorous terminology and concepts in dimensions we cannot visualize. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.

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