Q13 of 112 Page 1143

Find the shortest distance between the lines L1 and L2 whose vector equations are

and


HINT: The given lines are parallel.


Given equations :




To Find : d


Formula :


1. Cross Product :


If are two vectors




then,



2. Dot Product :


If are two vectors




then,



3. Shortest distance between two parallel lines :


The shortest distance between the parallel lines and


is given by,



Answer :


For given lines,




Here,






As , given lines are parallel to each other.


Therefore,






= 7










Therefore, the shortest distance between the given lines is





More from this chapter

All 112 →
11

Show that the lines and intersect.

Also, find their point of intersection.


 12

Show that the lines and intersect.

Also, find their point of intersection.


 14

Find the distance between the parallel lines L1 and L2 whose vector equations are and

15

Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line Also, find the distance between these lines.

HINT: The given line is



The required line is



Now, find the distance between the parallel lines L1 and L2.