6. The distance between two straight lines in space
Let there be given two lines in space: the first
line
passing through a point
and having a direction vector
,
and the second line
passing through a point
and having a direction vector
.
If the two lines are parallel then the distance between them may be
found as the distance from the point
to the line
or contrary. If
and
are skew lines then the distance d
between their closest points may be found as the high of the
parallelepiped formed on the vectors
,
and
by the following formula:
(7)
7. The closest points of two skew lines can be found as intersection points of the plane passing through the common perpendicular and one of the two lines with other line.
8. The point of intersection a plane and a straight line in space
Common point of a given plane and line can be found as the solution of the system of their equations:
9. The angle between a plane and a straight
line in space is equal to the
complementary angle of the angle between the normal vector
of the plane and the direction vector
of the line:
.