The Wayback Machine - https://web.archive.org/web/20140324031603/http://mathworld.wolfram.com/Perpendicular.html
Geometry > Surfaces > Planes >

Perpendicular

EXPLORE THIS TOPIC IN the MathWorld Classroom Perpendicular

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product

 a·b=0.
(1)

In R^2, a line with slope m_2=-1/m_1 is perpendicular to a line with slope m_1. Perpendicular objects are sometimes said to be "orthogonal."

In the above figure, the line segment AB is perpendicular to the line segment CD. This relationship is commonly denoted with a small square at the vertex where perpendicular objects meet, as shown above, and is denoted AB_|_CD.

Two trilinear lines

lalpha+mbeta+ngamma=0
(2)
l^'alpha+m^'beta+n^'gamma=0
(3)

are perpendicular if

 ll^'+mm^'+nn^'-(mn^'+m^'n)cosA-(nl^'+n^'l)cosB 
 -(lm^'+l^'m)cosC=0
(4)

(Kimberling 1998, p. 29).

Wolfram Web Resources

Mathematica »

The #1 tool for creating Demonstrations and anything technical.

Wolfram|Alpha »

Explore anything with the first computational knowledge engine.

Wolfram Demonstrations Project »

Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Computable Document Format »

The format that makes Demonstrations (and any information) easy to share and interact with.

STEM initiative »

Programs & resources for educators, schools & students.

Computerbasedmath.org »

Join the initiative for modernizing math education.