Difference between revisions of "Perpendicular"

(new article)
 
Line 1: Line 1:
To lines would be '''perpendicular''' if their intersection creates[[right angle]]s.  If a line has slope <math>m</math> then all lines perpendicular to it and none other have slope <math>-\frac{1}{m}</math>.
+
{{stub}}
 +
 
 +
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.
 +
 
 +
 
 +
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>. 
 +
 
 +
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 $l$ and $m$ are said to be perpendicular if they intersect in right angles. We denote this relationship by $l \perp m$. In the Cartesian coordinate system, a line with slope $m$ is perpendicular to every line with slope $-\frac{1}{m}$ and no others.


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

If a plane $P$ intersects another plane $Q$ in a line $k$, we say that $P \perp Q$ if and only if: for line $l \in P$ and $m \in Q$ passing through $A \in k$, $l \perp k$ and $m \perp k$ implies $l \perp m$.

Invalid username
Login to AoPS