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Example:Finding Distance of a Point from Plane

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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 3

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


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)




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.