UPSC NDA I 2019 Mathematics Solved Paper

(A)
Family of plane passing through line of intersection of planes
2x + y + 2z = 9 and 4x − 5y − 4z = 1 is (2x+ y+2 z−9) + λ (4 x−5 y−4 z−1) = 0 …(i)
This plane passes through (3,2, 1)
⇒ λ =

1

3

Hence equation of required plane is
(2x+ y+2 z−9) +

1

3

(4 x−5 y−4 z−1) = 0
⇒ 10 x − 2 y + 2z = 28