Book: Mathematics Part-II
Chapter: 11. Three Dimensional Geometry
Subject: Maths - Class 12th
Q. No. 15 of Exercise 11.2
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15
Find the shortest distance between the lines
We know that
Shortest distance between the lines:
and 
is
…(i)
The standard form of a pair of Cartesian lines is:
and 
And the given equations are: 
and 
Comparing the given equations with the standard form, we get
x1 = -1, y1 = -1, z1 = -1; x2 = 3, y2 = 5, z2 = 7
a1 = 7, b1 = -6, c1 = 1; a2 = 1, b2 = -2, c2 = 1
Now, consider
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Next, consider
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⇒ 
⇒ 
⇒ 
⇒ From (i), we have
⇒ 
15
