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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Point of Intersection Calculation

JEE Main asked Point of Intersection Calculation 8 times in 8 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Lines in 3D, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 1 year. In 2021 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
8
in 8 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210.04’220.07’230.09’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 20221 of 24
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Parameters from intersection of lines on coordinate plane
  • Area of triangle from intersecting lines

Difficulty

Easy 0Medium 6Hard 2

2 of the 8 questions had a numerical answer.

Every question

All 8 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  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. 4 Apr 2025, Shift 2 · Q15Let A be the point of intersection of the lines L1:x−71=y−50=z−3−1L_1:\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1} and…MediumSingle correct
  3. 29 Jan 2024, Shift 1 · Q16Let PQR be a triangle with R(−1,4,2)R(-1,4,2). Suppose M(2,1,2)M(2,1,2) is the mid point of PQ. The distance of the centroid of ΔPQR\Delta PQR from the…MediumSingle correct
  4. 5 Apr 2024, Shift 1 · Q17Let d be the distance of the point of intersection of the lines x+63=y2=z+11\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1} and…MediumSingle correct
  5. 10 Apr 2023, Shift 2 · Q15Let the line x1=6−y2=z+85\frac{x}{1} = \frac{6-y}{2} = \frac{z+8}{5} intersect the lines x−54=y−73=z+21\frac{x-5}{4} = \frac{y-7}{3} = \frac{z+2}{1} and…HardSingle correct
  6. 29 Jul 2022, Shift 1 · Q23Let a line with direction ratios a,−4a,−7a, -4a, -7 be perpendicular to the lines with direction ratios 3,−1,2b3, -1, 2b and b,a,−2b, a, -2. If the point…HardNumerical value
  7. 31 Aug 2021, Shift 1 · Q87The square of the distance of the point of intersection of the line x−12=y−23=z+16\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6} and the plane 2x−y+z=62x-y+z=6…MediumNumerical value
  8. 4 Aug 2021, Shift 2 · Q75The equation of a line passing through the point (2,−1,1)(2,-1,1) and the point of intersection of the lines 2x−y−4=0=y+2z2x-y-4=0=y+2z and…MediumSingle correct

Shifts: 4 Aug 2021, Shift 2, 31 Aug 2021, Shift 1, 29 Jul 2022, Shift 1, 10 Apr 2023, Shift 2, 29 Jan 2024, Shift 1, 5 Apr 2024, Shift 1, 4 Apr 2025, Shift 2, 2 Apr 2026, Shift 1.

Same topic

Other ideas in Lines in 3D

Lines in 3D has 18 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas