Book: Mathematics Part-II
Chapter: 11. Three Dimensional Geometry
Subject: Maths - Class 12th
Q. No. 9 of Miscellaneous Exercise
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9
Find the shortest distance between lines
and 
.
Shortest distance between lines with vector equations
and 
is
⇒ 
Given -
Comparing with 
, we get -
& 
Similarly,
Comparing with 
, we get -
& 
Now,
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Magnitude of 
= 
= √144
= 12
Also,
⇒ 
= -80 + (-16) + (-12)
= -108
Shortest Distance 
= 9
Hence, the shortest distance between the given two lines is 9.
9
