Difference between revisions of "Plane"
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(Added information on mathematical expression of planes) |
(takes only three points to determine a plane, but) |
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| − | A plane is a flat surface | + | A plane is a flat surface with limitless area. |
| + | 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 = 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. | 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. | ||
Revision as of 19:10, April 7, 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.