Question
Find the shortest distance between the lines:
and 
Solution
The equations of the two lines are
...(1)
and
...(2)
Comparing these equations with
we get
Let S be the point on the line (1) with position vector
and T be the point on the line (2) with position vector 
Now,
Let
be the S.D. vector between given lines. Therefore, it is parallel to 
.
If
is a vector along 
then
Now. S.D. = Projection of
= Projection of 
...(1)and
...(2)Comparing these equations with
we getLet S be the point on the line (1) with position vector
and T be the point on the line (2) with position vector Now,
Let
be the S.D. vector between given lines. Therefore, it is parallel to .If
is a vector along thenNow. S.D. = Projection of
= Projection of
