Home | About Mathguru | Advertisements | Teacher Zone | FAQs | Contact Us | Login

 
If you like what you see in Mathguru
Subscribe Today
For 12 Months
US Dollars 12 / Indian Rupees 600
Available in 20 more currencies if you pay with PayPal.
Buy Now
No questions asked full moneyback guarantee within 7 days of purchase, in case of Visa and Mastercard payment
  

Example:Finding Intercepts Cut off by a Plane

Post to:

Bookmark and Share



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 3

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:

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.

 

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.

 

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

 

Let the equation of the plane be

Ax+ By+Cz = 0, D0

Intercepts a(a,0,0), b(0,b,0) and c(0,0,c) is given by

a = -

b = -

c = -