The distance between two skew lines with equations
 |  |  |
(1)
|
 |  |  |
(2)
|
is given by
![D=(|(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]|)/(|(x_2-x_1)x(x_4-x_3)|)](/images/equations/Line-LineDistance/NumberedEquation1.svg) |
(3)
|
(Gellert et al. 1989, p. 538). This can be written in the concise form
 |
(4)
|
by defining
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
Line-Line Distance
See also
Skew Lines, Line-Line Angle, Line-Line IntersectionExplore with Wolfram|Alpha
References
Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.Hill, F. S. Jr. "The Pleasures of 'Perp Dot' Products." Ch. II.5 in Graphics Gems IV (Ed. P. S. Heckbert). San Diego: Academic Press, pp. 138-148, 1994.Referenced on Wolfram|Alpha
Line-Line DistanceCite this as:
Weisstein, Eric W. "Line-Line Distance." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Line-LineDistance.html