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When the principle of a plane is extended into higher dimensions, it is known as a [[hyperplane]].
When the principle of a plane is extended into higher dimensions, it is known as a [[hyperplane]].
== How to find the equation of a plane from three points ==
Consider points A(x<sub>A</sub>, y<sub>A</sub>, z<sub>A</sub>), B(x<sub>B</sub>, y<sub>B</sub>, z<sub>B</sub>), and C(x<sub>C</sub>, y<sub>C</sub>, z<sub>C</sub>). How do you find the equation of the plane defined by those three points?
First, you must find the vector normal to the plane. This is found by calculating the [[cross product]] of two vectors in the plane.
vector AB = <(x<sub>B</sub> - x<sub>A</sub>), (y<sub>B</sub> - y<sub>A</sub>), (z<sub>B</sub> - z<sub>A</sub>)>
vector BC = <(x<sub>C</sub> - x<sub>B</sub>), (y<sub>C</sub> - y<sub>B</sub>), (z<sub>C</sub> - z<sub>B</sub>)>
AB cross BC = <D, E, F>
(D, E, and F stand for the numbers found when the cross product is calculated.)
The equation of the plane is then D(x - x<sub>A</sub>) + E(y - y<sub>A</sub>) + F(z - z<sub>A</sub>) = 0
(The coordinates of points B and C could have been used instead.)
[[Category:Geometry]]
[[Category:Geometry]]