Plane (mathematics)

In mathematics, a plane is the fundamental two-dimensional object. Intuitively, it may be visualized as a flat infinite piece of paper.\nMost 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\n* a line and a point not lying on the line\n* a point and a line, the normal to the plane\n* two lines which intersect in a single point or are parallel

In three-dimensional space, two different planes are either parallel or they intersect in a line. A line which is not parallel to a given plane intersects that plane in a single point. Category:Surfaces \n\n\n