I am trying to understand the Shortest dostance between two skew lines.
I know the process. But I can not understand the process. My doubts are following.
First: A line segment , which is perpendicular to both lines , is drawn . (My doubt — How you are sure to have a segment like that? There may not exist such kind of segment.)
Second: Two points P & Q, one from each line, are taken and we determine the length of the projection of PQ on the segment. The length of the projection on the segment , which is perpendicular to both the lines, is nothing but the length of the segment .This length is shortest distance. ( My question : PQ and the segment, which is perpendicular to both the lines, may not be coplanar. Then how we take the projection of PQ on the segment. )
Can someone please help me to clear my doubts?
Best Answer
Consider two parallel planes. The distance between these planes is the length of the common perpendicular segment connecting the two planes. Now if we draw two lines one on each plane we can define the distance between the lines to be the distance between the two parallel planes.
If you start with two sqew lines you can construct parallel planes on which these two lines locate.
Thus the distance between sqew lines is well defined and the process works as you have explained.