EQUATION OF SKEW LINES
SHORTEST DISTANCE BETWEEN SKEW LINES
Sorry guys! for this late blog. I know I promised to continue the wavelet series but due to some work, I am stuck with some projects. So I am sharing one of my old works on skew lines. Hope this enlightens you. Next week will be wavelets pakka! Enjoy friends!
INTRODUCTION
In three-dimensional space, if a point moves so that it maintains a fixed direction throughout its journey, then the locus is a straight line. Hence a straight line in space is uniquely determined by either
i.By a point on it and its direction
ii. By two points on it.
SKEW LINES: These are non-parallel, non-intersecting lines in two different planes. They are also called Agonic lines. The existence of these lines is marked through the opposite edges of a regular tetrahedron.
If present on the same plane must either cross each other or be parallel.
They can only exist in three or more dimensions
Skew lines are never coplanar.
The shortest distance is measured by the quickest route traversed by a point particle, applying no force, in the minimum time possible.
When two skew lines are concerned, provided with ample information, methods are devised to calculate the shortest distance from known entities.
Formula of the normal form of a pair of skew lines to find the shortest distance where l1,m1,n1 and l2,m2,n2 are the direction ratios:
Vector representation of skew lines:
Below are some animations showing skew line’s property:
