UPSC NDA Math Model Paper 3

Given: Equation of two lines is

1−x

3

=

7y−14

2k

=

z−3

2

and

7−7x

3k

=

5−y

1

=

6−z

5

The given equation can be re-written as:

⇒

x−1

−3

=

y−2

2k 7

=

z−3

2

and

x−1

−3k 7

=

y−5

−1

=

z−6

−5

The direction ratios of the given lines are:
⇒a1=−3,b1=2k∕7,c1=2, a2=−3k∕7,b2=−1 and c2=−5
∵ The given lines are perpendicular to each to each other
As we know that if two lines are perpendicular to each to each other then a1.a2+b1.b2+c1.c2=0
⇒a1a2+b1b2+c1c2 =−3.

−3k

7

+(

2k

7

) .(−1)+2.(−5)=0
⇒k=10