4. shortest distance between two lines

Shortest Distance between Two Lines:

1. If  lines are intersecting then the shortest distance is zero.
2. If  lines are skew lines , the line of the shortest distance will be perpendicular to both the lines.
3. If  lines are parallel  lines , the line of the shortest distance will be perpendicular distance.

Distance between two skew lines:

In  a space, there are lines which are neither intersecting nor parallel. In fact,such pair of lines are non coplanar and are called skew lines.

Vector Form                      

We shall consider two skew lines, say l₁ and l­₂ and we are to calculate the distance between them. The equations of the lines are:

where d measures the distance or the length of the perpendicular.

 

Cartesian form:

The shortest distance between the lines

Distance between parallel lines:

If two lines l1 and l2 are parallel, then they are coplanar.

 Let the lines be given by

Shortest distance between LINES