UPSC NDA Math Model Paper 7

Given lines are

x+4

2

=

4−y

−2

=

2z−4

2k

and

x+3

−k

=

y−3

2

=

z+1

5

Write the above equation of a line in the standard form of lines
⇒

x+4

2

=

−(y−4)

−2

=

2(z−2)

2k

⇔

(x+4)

2

=

y−4

2

=

z−2

k

So, the direction ratio of the first line is (2, 2, k)

x+3

−k

=

y−3

2

=

z+1

5

So, direction ratio of second line is (-k, 2, 5)
Lines are perpendicular,
∴(2×−k)+(2×2)+(k×5)=0
⇒−2k+4+5k=0
⇒3k+4=0
∴ k = -4/3