In mathematics, a plane is a 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
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 coordinate system
(x;y;z), one can define a plane as the set of all solutions of an
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 vectors defining the
A plane is uniquely determined by any of the following combinations:
- three points 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
- 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.