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Saturday, 31 October

JEE Main 2023 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let λ1,λ2\lambda_1,\lambda_2 be the values of λ\lambda for which the points (52,1,λ)\left(\frac{5}{2},1,\lambda\right) and (−2,0,1)(-2,0,1) are at equal distance from the plane 2x+3y−6z+7=02x+3y-6z+7=0. If λ1>λ2\lambda_1>\lambda_2, then the distance of the point (λ1−λ2,λ2,λ1)(\lambda_1-\lambda_2,\lambda_2,\lambda_1) from the line x−51=y−12=z+72\frac{x-5}{1}=\frac{y-1}{2}=\frac{z+7}{2} is __________.

Official answer

9

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Point-Plane Distance
Idea tested
Distance from Point

Same idea in other shifts

Asked 3× in all
  1. 10 Apr 2023, Shift 1 · Q14Let P be the point of intersection of the line x+33=y+21=1−z2\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2} and the plane x+y+z=2x+y+z=2. If the distance of the…MediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q77A plane intersects the yzyz-plane at x=0, 2y−3z=5x = 0,\ 2y - 3z = 5 and it intersects the xyxy-plane at z=0, 7x+4y=10z = 0,\ 7x + 4y = 10. Then the distance…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.