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Jay Jay the Jet Plane
In mathematics, a plane is a fundamental two-dimensional object. Intuitively, it may be visualized as a flat infinite sheet of paper. more...
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There are several definitions of the plane, equivalent in the sense of Euclidean geometry, but which can be extended in different ways to define objects in other areas of mathematics.
In some areas of mathematics, such as plane geometry or 2D computer graphics, the whole space in which the work is carried out is a single plane. In such situations, the definite article is used: the plane. Many fundamental tasks in geometry, trigonometry, and graphing are performed in the two dimensional space, or in other words, in the plane.
Euclidean geometry
A plane is a surface such that, given any three points on the surface, the surface also contains the straight line that passes through any two of them. One can introduce a Cartesian coordinate system on a given plane in order to label every point on it uniquely with two numbers, the point's coordinates.
Within any Euclidean space, a plane is uniquely determined by any of the following combinations:
three non-collinear points (not lying on the same line);
a line and a point not on the line;
two different lines which intersect;
two different lines which are parallel;
Planes embedded in ℝ3
This section is specifically concerned with planes embedded in three dimensions: specifically, in ℝ3.
Properties
In three-dimensional Euclidean space, we may exploit the following facts that do not hold in higher dimensions:
Two planes are either parallel or they intersect in a line.;
A line is either parallel to a plane or they intersect at a single point.;
Two lines normal (perpendicular) to the same plane must be parallel to each other.;
Two planes normal to the same line must be parallel to each other.;
Define a plane with a point and a normal vector
In a three-dimensional space, there is another important way of defining a plane:
A point and a normal vector to the plane;
We can describe the resulting plane.
Let 
If we write  Π is determined by the condition:
Read more at Wikipedia.org
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