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Perpendicular


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).


See also

Cathetus, Gnomon, Normal Vector, Orthogonal Lines, Orthogonal Vectors, Parallel, Perpendicular Bisector, Perpendicular Foot, Perpendicular Vector, Right Angle Explore this topic in the MathWorld classroom

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References

Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 10, 1948.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Perpendicular

Cite this as:

Weisstein, Eric W. "Perpendicular." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Perpendicular.html

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