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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

Let S be the mirror image of the point Q(1,3,4)Q(1, 3, 4) with respect to the plane 2x−y+z+3=02x - y + z + 3 = 0 and let R(3,5,γ)R(3, 5, \gamma) be a point of this plane. Then the square of the length of the line segment SR is __________.

Official answer

72

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Point-Plane Distance
Idea tested
Image of a Point

Same idea in other shifts

Asked 8× in all
  1. 10 Apr 2023, Shift 1 · Q13Let two vertices of a triangle ABC be (2,4,6)(2,4,6) and (0,−2,−5)(0,-2,-5), and its centroid be (2,1,−1)(2,1,-1). If the image of the third vertex in the…MediumSingle correct
  2. 25 Jun 2022, Shift 1 · Q17Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x+y+z=5x+y+z=5. If a line L passing through (1,−1,−1)(1,-1,-1),…MediumSingle correct
  3. 27 Jun 2022, Shift 1 · Q30Let the mirror image of the point (a,b,c)(a, b, c) with respect to the plane 3x−4y+12z+19=03x-4y+12z+19=0 be (a−6,β,γ)(a-6, \beta, \gamma). If a+b+c=5a+b+c=5, then…MediumNumerical value
  4. 29 Jun 2022, Shift 1 · Q3If the mirror image of the point (2,4,7)(2, 4, 7) in the plane 3x−y+4z=23x - y + 4z = 2 is (a,b,c)(a, b, c), then 2a+b+2c2a + b + 2c is equal to :EasySingle correct
  5. 26 Feb 2021, Shift 2 · Q61If the mirror image of the point (1,3,5)(1, 3, 5) with respect to the plane 4x−5y+2z=84x-5y+2z=8 is (α,β,γ)(\alpha, \beta, \gamma), then…EasySingle correct
  6. 18 Mar 2021, Shift 2 · Q88Let the mirror image of the point (1,3,a)(1, 3, a) with respect to the plane r⃗⋅(2i^−j^+k^)−b=0\vec{r}\cdot\left(2\hat{i}-\hat{j}+\hat{k}\right)-b=0 be…MediumNumerical value
  7. 2 Apr 2017 (offline) · Q83If the image of the point P(1,−2,3)P(1,-2,3) in the plane, 2x+3y−4z+22=02x+3y-4z+22=0 measured parallel to the line, x1=y4=z5\frac{x}{1}=\frac{y}{4}=\frac{z}{5}…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.