NDA 1 2025 Maths, question 65

Topic: Analytical geometry

Q65

What is the equation of the plane passing through the point $(1,1,1)$ and perpendicular to the line whose direction ratios are $(3,2,1)$ ?

(a) $x + 2y + 3z = 6$
(b) $3x + 2y + z = 6$ Correct answer
(c) $x + y + z = 3$
(d) $3x + 2y + z = 0$

Solution.

Answer: (b) $3x + 2y + z = 6$

A plane perpendicular to the given line has normal vector $(3,2,1)$ .
Its equation through $(1,1,1)$ is $3(x - 1) + 2(y - 1) + (z - 1) = 0$ .
Simplifying gives $3x + 2y + z = 6$ .