Shortest distance between two straight lines

Three Dimensional Geometry of Class 12

Shortest distance between two straight lines

Skew Lines

Two straight lines in space which are neither parallel nor intersecting are called skew lines.

Line of shortest distance

If l1 and l2 are two skew lines, then there is one and only one line perpendicular to each of lines l1 and l2 which is known as the line of shortest distance.

Shortest distance between two straight lines

Shortest distance

The shortest distance between two lines l1 and l2 is the distance PQ between the points P and Q where the lines of shortest distance intersects the two given lines.

Vector form

If Shortest distance between two straight lines and Shortest distance between two straight lines are two skew lines, then the shortest distance between these lines is d = Shortest distance between two straight lines

Cartesian Form

Let  Shortest distance between two straight lines   and Shortest distance between two straight lines are two skew lines, then shortest distance between these lines is given by

d = Shortest distance between two straight lines

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