Difference between revisions of "Plane"
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(takes only three points to determine a plane, but) |
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It takes only three [[point]]s to determine a plane, but they must be non-[[collinear]], i.e., they can't all be on the same line. | It takes only three [[point]]s to determine a plane, but they must be non-[[collinear]], i.e., they can't all be on the same line. | ||
| − | Mathematically, a plane takes the form Ax + By + Cz = | + | Mathematically, a plane takes the form Ax + By + Cz = Ax<sub>0</sub> + By<sub>0</sub> + Cz<sub>0</sub>, where the point (x<sub>0</sub>, y<sub>0</sub>, z<sub>0</sub>) is in the plane, and the three-dimensional [[vector]] <A, B, C> is normal (also orthogonal or [[perpendicular]]) to the plane. |
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]]. | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 02:11, April 20, 2007
A plane is a flat surface with limitless area. It takes only three points to determine a plane, but they must be non-collinear, i.e., they can't all be on the same line.
Mathematically, a plane takes the form Ax + By + Cz = Ax0 + By0 + Cz0, where the point (x0, y0, z0) is in the plane, and the three-dimensional vector <A, B, C> is normal (also orthogonal or perpendicular) to the plane.
When the principle of a plane is extended into higher dimensions, it is known as a hyperplane.