MathBin | Plane | Member |
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A plane is a two-dimensional object that exists in two dimensions or higher. Specifically, it is a flat, two-dimensional surface. A plane is the two-dimensional analogue to a point (zero dimensions) and a line (one dimension).

In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following:

- Three non-collinear points (points not on a single line).
- A line and a point not on that line.
- Two distinct but intersecting lines.
- Two parallel lines.

The following statements hold in three-dimensional Euclidean space but not in higher dimensions, though they have higher-dimensional analogues:

- Two distinct planes are either parallel or they intersect in a line.
- A line is either parallel to a plane, intersects it at a single point, or is contained in the plane.
- Two distinct lines perpendicular to the same plane must be parallel to each other.
- Two distinct planes perpendicular to the same line must be parallel to each other.

To find a plane given by three points involves finding the normal vector to the plane using those three points. There is no plane if the points are **collinear** (they are all on the same line).