JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

If 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 point P is

(1, -2, 3)

, then the area of the triangle PQR is equal to

(1) $\frac{2}{3}\sqrt{38}$
(2) $\frac{4}{3}\sqrt{38}$ Official answer
(3) $\frac{8}{3}\sqrt{38}$
(4) $\sqrt{\frac{152}{3}}$

Official answer

Option 2

NTA final key.

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
29 Jun 2022, Shift 1 · Q29Let $P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4$ be a plane. Let $P_2$ be another plane which passes through the points…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.