plane
In mathematics, a plane is a two-dimensional flat surface that extends infinitely in all directions
In mathematics, a plane is a two-dimensional flat surface that extends infinitely in all directions. It is often represented as a perfectly flat surface with no thickness. A plane can be thought of as an imaginary sheet that goes on forever in all directions.
A plane is defined by three non-collinear points, meaning three points that are not on the same line. These points are used to determine the orientation and position of the plane in space. Once these three points are chosen, they uniquely define the plane.
A plane can also be represented by a mathematical equation. The general equation of a plane in three-dimensional space is Ax + By + Cz + D = 0, where A, B, and C are real numbers representing the coefficients of the variables x, y, and z, and D is a constant term.
Planes are used in various mathematical concepts and equations. They play a significant role in geometry, particularly in the study of shapes and their properties. For example, the intersection of two planes can form a line, and the intersection of three planes may result in a single point. Additionally, planes are often utilized in linear algebra, calculus, and physics to model and solve problems related to vectors, functions, and equations in three-dimensional space.
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