Plane
A plane, in mathematics, refers to a flat, two-dimensional surface that extends infinitely in all directions
A plane, in mathematics, refers to a flat, two-dimensional surface that extends infinitely in all directions. It is a fundamental concept in geometry.
In geometry, a plane is defined by three non-collinear points. These points are not in a straight line and determine a unique plane. Once the plane is defined, it can be represented by an equation in the form Ax + By + Cz + D = 0, where A, B, and C are constants and x, y, and z represent the coordinates of any point on the plane.
Planes have several important properties:
1. Flatness: A plane does not have any curves or bends. It is completely flat and extends infinitely in all directions.
2. Infinite extent: A plane continues indefinitely in all directions. There is no boundary or edge to a plane.
3. Parallel lines: If two lines lie on the same plane, they are parallel and will never intersect.
4. Intersection: Two distinct planes can intersect in a line. The line is the common intersection of the two planes.
5. Angles: The angle between two planes is defined as the angle between their respective normal vectors. If the normal vectors are perpendicular, the planes are said to be perpendicular to each other.
Planes are widely used in various branches of mathematics, such as geometry, calculus, and linear algebra. They provide a fundamental framework for studying the relationship between points, lines, and shapes in a geometric space.
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