What is a Plane?
A Plane in three-dimensional (3D) geometry is a surface such that the line segment joining any two points lies completely on it. It is the collection of all the points and can be extended infinitely in any of the two dimensions.
The general form of a plane in 3D is a first-degree equation in x, y, z i.e. We represent a plane in 3-D as,
(ax + by + cz + d = 0)
where
(x, y, z) represents the coordinates of a variable point on the plane.
A plane has only two dimensions length and breadth and it can be infinitely stretched in these two dimensions.
Read More, Cartesian Plane
Points, Lines and Planes
Points, Lines, and Planes are basic terms used in Geometry that have a specific meaning and are used to define the basis of geometry. We define a point as a location in 3-D or 2-D space that is represented using the coordinates.
We define a line as a geometrical figure that is extended in both directions to infinity. Similarly, a plane is defined as the collection of all such lines, i.e. it is a 3-D space on which the line passes.
In this article, we will learn about Points, Lines, and Planes in detail including their solved examples and problems based on them.
Table of Content
- Points, Lines, and Planes in Geometry
- What is a Point?
- Collinear and Non-Collinear Points
- Coplanar and Non-Coplanar Points
- What is a Line?
- Line Segment
- Mid-Point
- Rays
- Intersecting and Parallel lines
- Perpendicular Lines
- What is a Plane?
- Solid
- Vector Form of Equation of Plane in Normal Form
- Cartesian Form of Equation of a Plane in Normal Form
- Distance of a Point from a Plane in Cartesian Form
- Distance of a Point from a Plane in Vector Form
- Points, Lines, and Planes Solved Examples
- Points, Lines and Planes Worksheet