JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let

P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4

be a plane. Let

P_2

be another plane which passes through the points

(2, -3, 2)

(2, -2, -3)

and

(1, -4, 2)

. If the direction ratios of the line of intersection of

P_1

and

P_2

16, \alpha, \beta

, then the value of

\alpha + \beta

is equal to ____________.

Official answer

NTA final key (2022 Session 1).

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Direction of Line of Intersection

Same idea in other shifts

Asked 4× in all

26 Jul 2022, Shift 2 · Q15A vector $\vec{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i},\ \hat{i}+\hat{j}$ and the…MediumSingle correct
27 Jul 2022, Shift 2 · Q15If the line of intersection of the planes $ax + by = 3$ and $ax + by + cz = 0$ , a > 0 makes an angle $30^\circ$ with the plane…MediumSingle correct
28 Jun 2022, Shift 1 · Q15If two distinct points Q, R lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the…HardSingle correct

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.