NDA 2 2025 Maths, question 52

Topic: Analytical geometry

Passage · Q51 to Q52

A plane $P$ is parallel to the line having direction ratios $⟨1,3,2⟩$ and contains the line of intersection of the planes $6x+4y-5z=2$ and $x-2y+3z=0$ .

Q52

What is the equation of the plane $P$ ?

(a) $2x-20y+29z+2=0$ Correct answer
(b) $2x-20y+29z-2=0$
(c) $2x+3y+2z-4=0$
(d) $x-3y+2z+5=0$

Solution.

Answer: (a) $2x-20y+29z+2=0$

A plane through the intersection is (6x+4y−5z−2)+λ(x−2y+3z)=0.
Its normal dotted with (1,3,2) is 8+λ.
Parallelism requires λ=−8, giving −2x+20y−29z−2=0, equivalent to option (a).