JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

P

be the plane passing through the intersection of the planes

\vec{r} \cdot \left(\hat{i} + 3\hat{j} - \hat{k}\right) = 5

and

\vec{r} \cdot \left(2\hat{i} - \hat{j} + \hat{k}\right) = 3

, and the point

(2, 1, -2)

. Let the position vectors of the points

X

and

Y

be ,

\hat{i} - 2\hat{j} + 4\hat{k}

and

5\hat{i} - \hat{j} + 2\hat{k}

respectively. Then the points

(1) $X$ and $X + Y$ are on the same side of $P$
(2) $Y$ and $Y - X$ are on the opposite sides of $P$
(3) $X$ and $Y$ are on the opposite sides of $P$ Official answer
(4) $X + Y$ and $X - Y$ are on the same side of $P$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Relative Position of Two Points

Same topic in other shifts

All Planes in 3D questions

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.