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