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Example:Finding Coordinates of Foot of Perpendicular

 Post to:   Explanation:

Plane (geometry) Two intersecting planes in three-dimensional space

In mathematics, a plane is any flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line(one-dimension) and a space (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

## Planes embedded in ℝ3

This section is specifically concerned with planes embedded in three dimensions: specifically, in 3.

### 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, intersects it at a single point, or is contained in the plane.

§  Two lines perpendicular to the same plane must be parallel to each other.

§  Two planes perpendicular to the same line must be parallel to each other.

http://en.wikipedia.org/wiki/Plane_(geometry)

(Our solved example in mathguru.com uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

The Cartesian equation of the plane in normal form is

lx+ my+ nz = d

where l, m and n are the direction cosines