Perpendicular: Difference between revisions
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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. | |||
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 
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 .
