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 ℝ^{3}
This section is specifically concerned with planes embedded in
three dimensions: specifically, in ℝ^{3}.
Properties
In three-dimensional Euclidean space, we may exploit the following
facts that do not hold in higher dimensions:
1. Two
planes are either parallel or they intersect in a line.
2. A line
is either parallel to a plane, intersects it at a single point, or is contained
in the plane.
3. Two
lines perpendicular to the same plane must be parallel to
each other.
4. Two
planes perpendicular to the same line must be parallel to each other.
Distance from a point to
a plane
For a plane and a point not necessarily lying on
the plane, the shortest distance from to the plane is
It follows that lies
in the plane if and only if D=0.
If meaning that a, b, and c are
normalized then the equation becomes
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Plane_(geometry)
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons
Attribution- ShareAlike 3.0 Unported License.