Generally, three points in space will uniquely define a plane whereas **two points will not**. However, the three points must all be distinct and they must not lie on a straight line or else they behave like two points. The easiest way to check for collinearity is to compare the vectors joining pairs of the points.

## How many points do you need to define a plane?

In a three-dimensional space, a plane can be defined by **three points** it contains, as long as those points are not on the same line.

## How many planes are 2 points?

Solution. Given two distinct points, we can draw many planes passing through them. Therefore, **infinite number of planes** can be drawn passing through two distinct points or two points can be common to infinite number of planes.

## Do 2 vectors define a plane?

**A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors**.

## Can 4 points make a plane?

**Four points (like the corners of a tetrahedron or a triangular pyramid) will not all be on any plane**, though triples of them will form four different planes. Stepping down, two points form a line, and there wil be a fan of planes with this line (like pages of an open book, with the line down the spine of the book).

## How can I prove my flight?

- Three non-collinear points (points not on a single line).
- A line and a point not on that line.
- Two distinct but intersecting lines.
- Two distinct but parallel lines.

## How many planes can contain a point?

**Infinitely many** planes can be drawn through a single line or a single point. In the figure below, three of the infinitely many distinct planes contain line m and point A. Points and lines lying in the same plane are called coplanar.

## What is a real world example of a plane?

Examples of a plane would be: **a desktop, the chalkboard/whiteboard, a piece of paper, a TV screen, window, wall or a door**.

## How many planes can you draw through a line?

Given a line and a distinct point not lying on the line, **only a single plane** can be drawn through both of them as there can be only plane which can accommodate both the line and the point together. Let us take a line l and a point A, as we can see there can be only plane which pass through both of them.

## Is a plane an undefined term?

**In geometry, point, line, and plane are considered undefined terms** because they are only explained using examples and descriptions.

## Can points be coplanar?

**Points or lines are said to be coplanar if they lie in the same plane**. Example 1: The points P , Q , and R lie in the same plane A . They are coplanar .

## How do you make a plane with two lines?

**Points or lines are said to be coplanar if they lie in the same plane**. Example 1: The points P , Q , and R lie in the same plane A . They are coplanar .

### References:

- https://www.khanacademy.org/math/geometry-home/geometry-lines/points-lines-planes/v/specifying-planes-in-three-dimensions
- https://www.shaalaa.com/question-bank-solutions/how-many-planes-can-be-made-pass-through-two-points-euclid-s-definitions-axioms-postulates_62649
- https://mathworld.wolfram.com/Plane.html
- http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/gabrielle1.html
- https://en.wikipedia.org/wiki/Plane_(geometry)
- https://www.math.net/plane
- https://www.ck12.org/book/ck-12-geometry-second-edition/section/1.1/
- https://www.shaalaa.com/question-bank-solutions/how-many-planes-can-be-made-pass-through-line-point-not-line-euclid-s-definitions-axioms-postulates_62648
- http://www.chisd.net/cms/lib5/TX01917715/Centricity/Domain/402/Unit%2001%20Lesson%2001%20Points%20Lines%20and%20Planes.pptx
- https://www.varsitytutors.com/hotmath/hotmath_help/topics/coplanar
- https://www.youtube.com/watch?v=GQYIX8rjy5s