The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :

$$\pi - {\cos ^{ - 1}}\left( {{4 \over 9}} \right)$$

$${\cos ^{ - 1}}\left( {{8 \over 9}} \right)$$

3D Geometry — JEE Main Previous Year Questions

165 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 165
Years covered: 2016–2026
Avg / year: ~17
Subject: Mathematics

How many JEE Main questions come from 3D Geometry?

3D Geometry has contributed 165 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 17 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 165 questions carries a written, step-by-step solution, and each is tagged to 3D Geometry within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample 3D Geometry questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 165 3D Geometry questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2021
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :
1. (A) $\frac{π}{2}$
2. (B) $π - cos^{- 1} (\frac{4}{9})$
3. (C) $cos^{- 1} (\frac{8}{9})$
4. (D) $\frac{π}{3}$
Show answerAnswer
$Answer: (A) \frac{π}{2}$
Question 2 · JEE Main 2019
If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :
1. (A) $ab' + bc' + 1 = 0$
2. (B) $cc' + a + a' = 0$
3. (C) $bb' + cc' + 1 = 0$
4. (D) $aa' + c + c' = 0$
Show answerAnswer
$Answer: (D) aa' + c + c' = 0$
Question 3 · JEE Main 2019
If a point R(4, y, z) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10), then the distance of R from the origin is :
1. (A) $214$
2. (B) $53$
3. (C) $221$
4. (D) $6$
Show answerAnswer
$Answer: (A) 214$
Question 4 · JEE Main 2026
The square of the distance of the point $P (5, 6, 7)$ from the line $\frac{x - 2}{2} = \frac{y - 5}{3} = \frac{z - 2}{4}$ is equal to:
1. (A) $3$
2. (B) $5$
3. (C) $6$
4. (D) $8$
Show answerAnswer
$Answer: (C) 6$
Question 5 · JEE Main 2026
The shortest distance between the lines $\frac{x - 4}{1} = \frac{y - 3}{2} = \frac{z - 2}{- 3}$ and $\frac{x + 2}{2} = \frac{y - 6}{4} = \frac{z - 5}{- 5}$ is:
1. (A) $\frac{5 6}{6}$
2. (B) $25$
3. (C) $35$
4. (D) $45$
Show answerAnswer
$Answer: (C) 35$

3D Geometry questions by year

Year	Questions	Share of chapter questions
2026	29
2025	34
2024	43
2023	20
2022	15
2021	11
2020	4
2019	5
2018	2
2016	2

Practise these 165 questions with solutions

Free to start — 25 past-year questions a day with full written solutions, no card needed.

Start 3D Geometry practice free

FAQs

How many JEE Main questions have been asked from 3D Geometry?

EByAi's bank holds 165 real JEE Main questions from 3D Geometry, asked between 2016 and 2026 — about 17 per year on average. Every count is measured from actual papers, not estimated.

Is 3D Geometry important for JEE Main?

165 questions over 10 papers make 3D Geometry a moderate-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve 3D Geometry PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

More JEE Main Mathematics chapters

All JEE Main Mathematics chapters →JEE Main overview →