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