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Example:Finding Shortest distance

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Explanation:

 

Skew lines

 

In solid geometry, skew lines are two lines that do not intersect and are not parallel. Equivalently, they are lines that are not coplanar. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron. Lines that are coplanar either intersect or are parallel, so skew lines exist only in three or more dimensions.

 

Distance between two skew lines

To calculate the distance between two skew lines the lines are expressed using vectors,

.

The cross product of b and d is perpendicular to the lines, as is the unit vector

(if |b × d| is zero the lines are parallel and this method cannot be used). The distance between the lines is then

.

(Our solved example in mathguru.com uses this concept)

 

 

http://en.wikipedia.org/wiki/Skew_lines

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.