Class 12 Maths Three Dimensional Geometry Shortest Distance between two lines

Shortest Distance between two lines

If two lines intersect at a point, then the shortest distance between is 0.

If two lines are parallel, then the shortest distance between will be given by the length of the perpendicular drawn from a point on one line form another line.

Skew Lines

Skew lines are the lines which are neither intersecting nor parallel.

In 2-D lines are either parallel or intersecting. There are no skew lines in 2-D.

But in case of 3-D there are lines which are neither intersecting nor parallel to each other.

For skew lines, the line of the shortest distance will be perpendicular to both the lines.

From the figure we can see when we consider one line in xy plane and one in xz plane.We can see that these lines will never meet.

 

Shortest Distance between Two Skew Lines (Vector form)

 

Shortest Distance between Two Skew lines (Cartesian form)

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