Distance Between Two Lines

Distance Between Parallel Lines

The distance from a line, r, to another parallel line, s, is the distance from any point from r to s.

Distance Between Parallel Lines

Distance between Parallel Lines Formula

Distance Between Skew Lines

The distance between skew lines is measured on the common perpendicular.

If Distance Between Two Lines Example and Distance Between Two Lines Example determine the lines r and s.

Parallelepiped

The vectors Vectors determine the parallelepiped whose height is the distance between the two lines.

The volume of a parallelepiped is Volume of a Parallelepiped.

Given that the volume is the absolute value of the triple product of three vectors and the area of the base is the cross product of the direction vectors of the lines, the height is the distance between two points equal to:

Distance between Lines


Example

Find the minimum distance between the following lines:

Distance Between Two Lines Example

Linear Determination

Distance Between Two Lines Example

Linear Determination

Cross Product

Vectorial Product

Operations

Distance Between Two Lines Example