# Difference between revisions of "Perpendicular"

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+ | Two [[line]]s <math>l</math> and <math>m</math> are said to be '''perpendicular''' if they intersect in [[right angle]]s. We denote this relationship by <math>l \perp m</math>. In the [[Cartesian coordinate system]], a line with [[slope]] <math>m</math> is perpendicular to every line with slope <math>-\frac{1}{m}</math> and no others. | ||

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+ | One can also discuss perpendicularity of other objects. If a line <math>l</math> intersects a plane <math>P</math> at a point <math>A</math>, we say that <math>l \perp P</math> if and only if for ''every'' line <math>m</math> in <math>P</math> passing through <math>A</math>, <math>l \perp m</math>. | ||

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+ | If a plane <math>P</math> intersects another plane <math>Q</math> in a line <math>k</math>, we say that <math>P \perp Q</math> if and only if: | ||

+ | for line <math>l \in P</math> and <math>m \in Q</math> passing through <math>A \in k</math>, <math>l \perp k</math> and <math>m \perp k</math> implies <math>l \perp m</math>. |

## Revision as of 09:35, 23 August 2006

*This article is a stub. Help us out by expanding it.*

Two lines and are said to be **perpendicular** if they intersect in right angles. We denote this relationship by . In the Cartesian coordinate system, a line with slope is perpendicular to every line with slope and no others.

One can also discuss perpendicularity of other objects. If a line intersects a plane at a point , we say that if and only if for *every* line in passing through , .

If a plane intersects another plane in a line , we say that if and only if: for line and passing through , and implies .