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Friday, 9 October

JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2026, Shift 2, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let the foot of perpendicular from the point (λ,2,3)(\lambda, 2, 3) on the line x−41=y−92=z−51\frac{x-4}{1} = \frac{y-9}{2} = \frac{z-5}{1} be the point (1,μ,2)(1, \mu, 2). Then the distance between the lines x−12=y−23=z+46\frac{x-1}{2} = \frac{y-2}{3} = \frac{z+4}{6} and x−λ2=y−μ3=z+56\frac{x-\lambda}{2} = \frac{y-\mu}{3} = \frac{z+5}{6} is equal to :
  1. (1)127\frac{12}{7}
  2. (2)1457\frac{\sqrt{145}}{7}
  3. (3)1467\frac{\sqrt{146}}{7}Official answer
  4. (4)1437\frac{\sqrt{143}}{7}

Official answer

Option 3

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Shortest Distance Between Parallel Lines

Same topic in other shifts

All Lines in 3D questions
  1. 2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines x+13=y+a5=z+b+17\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7} and x−21=y−b4=z−2a7\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}…MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q15Let a line L passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i+2\hat j+\hat k and…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q15Let the point AA be the foot of perpendicular drawn from the point P(a,b,0)P(a, b, 0) on the line…MediumSingle correct
  4. 4 Apr 2026, Shift 1 · Q14A line with direction ratios 1,−1,21,-1,2 intersects the lines x2=y3=z+13\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3} and…MediumSingle correct
  5. 4 Apr 2026, Shift 2 · Q14If (2α+1, α2−3α, α−12)\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line…MediumSingle correct
  6. 5 Apr 2026, Shift 1 · Q13The square of the distance of the point P(5,6,7)P(5, 6, 7) from the line x−22=y−53=z−24\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4} is equal to:EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.