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