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JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

\frac{x - 2}{3} = \frac{y + 1}{-2} = \frac{z + 3}{-1}

lie on the plane

px - qy + z = 5

, for some

p, q \in \mathbb{R}

. The shortest distance of the plane from the origin is:

(1) $\sqrt{\frac{3}{109}}$
(2) $\sqrt{\frac{5}{142}}$ Official answer
(3) $\frac{5}{\sqrt{71}}$
(4) $\frac{1}{\sqrt{142}}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Condition for Line to Lie in Plane

Same idea in other shifts

Asked 2× in all

31 Aug 2021, Shift 2 · Q90Suppose the line $\frac{x-2}{\alpha} = \frac{y-2}{-5} = \frac{z+2}{2}$ lies on the plane $x+3y-2z+\beta = 0$ . Then $(\alpha+\beta)$ is…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.