# Plane (mathematics)

In mathematics, a plane is the fundamental two-dimensional object. Intuitively, it may be visualized as a flat infinite piece of paper. Most of the fundamental work in geometry, trigonometry, and graphing is performed in two dimensions, or in other words, in a plane.Given a plane, one can introduce a Cartesian coordinate system on it in order to label every point on the plane uniquely with two numbers, its coordinates.

In a three-dimensional *x*-*y*-*z* coordinate system, one can define a plane as the set of all solutions of an equation *ax* + *by* + *cz* + *d* = 0, where *a*, *b*, *c* and *d* are real numbers such that not all of *a*, *b*, *c* are zero. Alternatively, a plane may be described parametrically as the set of all points of the form **u** + *s* **v** + *t* **w** where *s* and *t* range over all real numbers, and **u**, **v** and **w** are given vectorss defining the plane.

A plane is uniquely determined by any of the following combinations:

- three pointss not lying on a line
- a line and a point not lying on the line
- a point and a line, the normal to the plane
- two lines which intersect in a single point or are parallel