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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 27 August 2021, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

The equation of the plane passing through the line of intersection of the planes r⃗⋅(i^+j^+k^)=1\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 and r⃗⋅(2i^+3j^−k^)+4=0\vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 and parallel to the xx-axis is :
  1. (1)r⃗⋅(i^−3k^)+6=0\vec{r} \cdot (\hat{i} - 3\hat{k}) + 6 = 0
  2. (2)r⃗⋅(i^+3k^)+6=0\vec{r} \cdot (\hat{i} + 3\hat{k}) + 6 = 0
  3. (3)r⃗⋅(j^−3k^)−6=0\vec{r} \cdot (\hat{j} - 3\hat{k}) - 6 = 0
  4. (4)r⃗⋅(j^−3k^)+6=0\vec{r} \cdot (\hat{j} - 3\hat{k}) + 6 = 0Official answer

Official answer

Option 4

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
  1. 6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes 2x−y+z=32x-y+z=3, 4x−3y+5z+9=04x-3y+5z+9=0 and parallel to the line…MediumSingle correct
  2. 6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane r⃗⋅(i^+j^+k^)=6\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6 and…MediumSingle correct
  3. 13 Apr 2023, Shift 1 · Q8Let the equation of plane passing through the line of intersection of the planes x+2y+az=2x+2y+az=2 and x−y+z=3x-y+z=3 be 5x−11y+bz=6a−15x-11y+bz=6a-1. For…MediumSingle correct
  4. 26 Jul 2022, Shift 2 · Q27The plane passing through the line L:lx−y+3(1−l)z=1, x+2y−z=2L: lx-y+3(1-l)z=1,\ x+2y-z=2 and perpendicular to the plane 3x+2y+z=63x+2y+z=6 is 3x−8y+7z=43x-8y+7z=4. If θ\theta…HardNumerical value
  5. 27 Jul 2022, Shift 1 · Q17If the plane PP passes through the intersection of two mutually perpendicular planes 2x+ky−5z=12x + ky - 5z = 1 and 3kx−ky+z=53kx - ky + z = 5, k<3k < 3…MediumSingle correct
  6. 28 Jun 2022, Shift 1 · Q16The acute angle between the planes P1_1 and P2_2, when P1_1 and P2_2 are the planes passing through the intersection of the planes…MediumSingle correct
  7. 28 Jun 2022, Shift 1 · Q17Let the plane P:r⃗⋅a⃗=dP:\vec{r}\cdot\vec{a}=d contain the line of intersection of two planes…HardSingle correct
  8. 26 Aug 2021, Shift 1 · Q75A plane P contains the line x+2y+3z+1=0=x−y−z−6x+2y+3z+1=0=x-y-z-6, and is perpendicular to the plane −2x+y+z+8=0-2x+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.