JEE Main 2021 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 24 February 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

The vector equation of the plane passing through the intersection of the planes

\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k})=1

and

\vec{r}\cdot(\hat{i}-2\hat{j})=-2

, and the point (1, 0, 2) is :

(1) $\vec{r}\cdot(3\hat{i}+7\hat{j}+3\hat{k})=7$
(2) $\vec{r}\cdot(\hat{i}+7\hat{j}+3\hat{k})=7$ Official answer
(3) $\vec{r}\cdot(\hat{i}-7\hat{j}+3\hat{k})=\frac{7}{3}$
(4) $\vec{r}\cdot(\hat{i}+7\hat{j}+3\hat{k})=\frac{7}{3}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Family of Planes

Same idea in other shifts

Asked 15× in all

6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…MediumSingle correct
6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and…MediumSingle correct
13 Apr 2023, Shift 1 · Q8Let the equation of plane passing through the line of intersection of the planes $x+2y+az=2$ and $x-y+z=3$ be $5x-11y+bz=6a-1$ . For…MediumSingle correct
26 Jul 2022, Shift 2 · Q27The plane passing through the line $L: lx-y+3(1-l)z=1,\ x+2y-z=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$ . If $\theta$ …HardNumerical value
27 Jul 2022, Shift 1 · Q17If the plane $P$ passes through the intersection of two mutually perpendicular planes $2x + ky - 5z = 1$ and $3kx - ky + z = 5$ , $k < 3$ …MediumSingle correct
28 Jun 2022, Shift 1 · Q16The acute angle between the planes P $_1$ and P $_2$ , when P $_1$ and P $_2$ are the planes passing through the intersection of the planes…MediumSingle correct
28 Jun 2022, Shift 1 · Q17Let the plane $P:\vec{r}\cdot\vec{a}=d$ contain the line of intersection of two planes…HardSingle correct
26 Aug 2021, Shift 1 · Q75A plane P contains the line $x+2y+3z+1=0=x-y-z-6$ , and is perpendicular to the plane $-2x+y+z+8=0$ . Then which of the following points…MediumSingle 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.