JEE Main Vector & 3D Questions 2027: Previous Year Questions, Weightage, Important Topics & Practice Paper

Joint Entrance Exam (JEE) Main 2026 ( JEE Main )

Mamona
Mamona Majumder
Deputy Manager
Updated on Aug 24, 2026 17:05 IST
Vectors and Three-Dimensional (3D) Geometry remain the single highest-scoring, high-weightage unit in the JEE Main Mathematics section. Contributing 3 to 4 questions per shift (12 to 16 marks) consistently from 2022 to 2026, mastering these two topics guarantees nearly 15% of the total Mathematics score.

Vectors and 3D have always been an integral part of the NTA JEE Main exam. Each shift features at least 3 to 4 questions every year. Therefore, it is important to understand the type of questions asked, concepts repeated most frequently and how to ace these two chapters from the JEE syllabus. Know everything in this article.

JEE Main Vector & 3D Questions

JEE Mains 2027 Vector & 3D Questions

JEE Main Vector & 3D Questions 2027: Vectors and Three-Dimensional (3D) Geometry remain the single highest-scoring, high-weightage unit in the JEE Main Mathematics section. Contributing 3 to 4 questions per shift (12 to 16 marks) consistently from 2022 to 2026, mastering these two topics guarantees nearly 15% of the total Mathematics score. Vectors and 3D questions are calculation-heavy (determinants & cross products). To ace these two chapters from JEE Mains 2027 syllabus, candidates should time their practice (example: 2.5 minutes per question).

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Table of contents
  • Key Highlights for JEE Main 3D and Vector Questions
  • JEE Mains 2027 Vector & 3D Geometry Questions
  • JEE Main Vectors & 3D Geometry Weightage: 5-Year Trend Analysis (2022 to 2026)
  • JEE Mains 3D and Vector Concept-Wise Weightage (2022 to 2026)
  • Preparation Strategy for 3D & Vectors Chapters for JEE Main 2027
  • High Probability JEE Main 2027 Vector and 3D Questions

Key Highlights for JEE Main 3D and Vector Questions

Shiksha experts have carefully analysed the past 5 year JEE Main question papers. The following observation has been made for the vector and 3D questions asked in the exam:

  • Consistent appearance each year: 100% of shifts in JEE Main 2025 and 2026 contained at least 3 questions from this unit, with roughly 40% of shifts featuring 4 questions.
  • Most repeated concept: Shortest distance between two skew lines appeared in over 85% of all shifts over the last 5 years.
  • Lengthy vs Tricky: Vector questions tend to be algebraic and identity-heavy (tricky), whereas 3D Geometry questions are calculation-intensive (lengthy).

JEE Mains 2027 Vector & 3D Geometry Questions

From below, candidates can download the JEE Main questions for vectors and three-dimensional geometry chapters. These questions have been curated from the past 5 year JEE Mains question papers.

Q1. Let O be the origin. Let OP = x i + y jk and OQ = − i + 2 j + 3 x k, x, y ∈ ℝ, x > 0, be such that | PQ| = √ 20 and the vector OP is perpendicular to OQ. If OR = 3 i + z j − 7 k, z ∈ ℝ, is coplanar with OP and OQ, then the value of x 2 + y 2 + z 2 is equal to:
(1) 9
(2) 2
(3) 7
(4) 1
 
Q2. If the equation of the plane passing through the mirror image of point (2, 3, 1) with respect to the line x + 12 = y − 1−1 = z + 23 and containing the line x − 23 = 1 − y2 = z + 11 is α x + β y + γ z = 24, then α + β + γ is equal to:
(1) 20
(2) 19
(3) 18
(4) 21
 
Q3. A vector a has components 3 p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If, with respect to the new system, a has components p + 1 and √ 10, then a value of p is equal to:
(1) −1
(2) 54
(3) − 54
(4) 1
 
Q4. Let a and b be two non-zero vectors perpendicular to each other and | a| = | b|. If | a × b| = | a|, then the angle between the vectors ( a + b + ( a × b)) and a is equal to:
(1) sin −1( 13)
(2) sin −1( 16)
(3) cos −1( 13)
(4) cos −1( 12)
 
Q5. In a triangle ABC, if | BC| = 8, | CA| = 7, and | AB| = 10, then the projection of vector AB on AC is equal to:
(1) 8514
(2) 254
(3) 12720
(4) 11516
 
Q6. For three unit vectors a, b, c satisfying | ab| 2 + | bc| 2 + | ca| 2 = 9 and |2 a + k b + k c| = 3, the positive value of k is:
(1) 6
(2) 4
(3) 3
(4) 5
 
Q7. If the distances of the point (1, 2, a) from the line x − 12 = y1 = z − 13 along the lines L 1 : x − 11 = y − 24 = zac and L 2 : x − 1b = y − 23 = za4 are equal, then a + b + c is equal to:
(1) 7
(2) 4
(3) 6
(4) 5
 
Q8. The perpendicular distance of the line x − 21 = y + 2−1 = z + 32 from the point P(2, −10, 1) is:
(1) 4√ 3
(2) 3√ 5
(3) 5√ 2
(4) 6
 
Q9. Let a and b be two unit vectors such that the angle between them is π3. If λ a + 2 b and 3 a − λ b are perpendicular to each other, then the number of values of λ in [−1, 3] is:
(1) 1
(2) 2
(3) 3
(4) 0
 
Q10. Let a line pass through two distinct points P(−2, 1, −3) and Q, and be parallel to the vector 3 i + 2 j + 2 k. If the distance of the point Q from the point R(1, 3, 3) is 5, then the square of the area of Δ PQR is equal to:
(1) 144
(2) 136
(3) 140
(4) 148

JEE Main Vectors & 3D Geometry Weightage: 5-Year Trend Analysis (2022 to 2026)

Check below the overall weightage of 3D and Vectors in JEE Mains exam from 2026 to 2022:

Year and Total Shifts

Vector Algebra (Total Qs)

3D Geometry (Total Qs)

Avg Qs per Shift

Weightage in Maths (%)

2026 - 20 (Jan & Apr)

36

42

3 to 4

13.0%

2025 - 20 (Jan & Apr)

34

44

3 to 4

13.0%

2024 - 20 (Jan & Apr)

31

45

3 to 4

12.6%

2023 - 24 (Jan & Apr)

38

58

4

13.3%

2022 - 22 (Jun & Jul)

32

52

3 to 4

12.7%

JEE Mains 3D and Vector Concept-Wise Weightage (2022 to 2026)

The vectors and 3D chapters contain subtopics or concepts. Not all subtopics carry equal weightage - some carry more weightage (frequency/yield). We have analysed which topics and concepts from vectors and 3D geometry have been asked most frequently in the past 5 years in the JEE Main exam. Check below:

Concept Area

Sub-Topics

Frequency / Yield

Average Difficulty

Shortest Distance & Skew Lines

Shortest distance between two skew lines in three-dimensional space and Parallel line distance

Very High (Every Shift)

Moderate

Vector Products & Linear Comb.

Scalar Triple Product, Vector Triple Product, Coplanarity

Very High (35% of Vector Qs)

Moderate to Tough

Image & Foot of Perpendicular

Point with respect to Line, Reflection across Line

High

Moderate

Line Intersection & Collinearity

Point of intersection, Coplanar lines in symmetric form

High

Easy to Moderate

Vector Projections & Geometry

Component of vector along/perp to another, Angle bisectors

Moderate

Easy

Planes (Pre-2024 Syllabus / Rare)

Family of planes, line-plane intersection

Low (Zero in 2024–2026)

Removed from Core

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Commonly asked questions
Q:   Is there negative marking in JEE Main?
A: 

Yes, JEE Main exam has negative marking. 1 mark is deducted for every incorrect answer.

Q:   Which mock tests are best for JEE Mains?
A: 

Best free mock tests for JEE Mains are previous year question papers. You can also practice NTA mock tests online at nta.ac.in. All mock tests are designed as per JEE Main syllabus and exam pattern.

Q:   What is the sequence of sections in the JEE Mains question paper?
A: 

Usually, in the JEE Mains computer-based exam, questions from maths are presented first, followed by Physics and Chemistry.

But candidates can appear for any section first, as per their preference.

Q:   Do I need to attempt all the questions in JEE Main exam?
A: 

NO, it is compulsory to attempt all questions in the JEE Main exam. The JEE Main exam has negative marking and candidates must answer only those questions for which they know the correct answer. Students must note that there are no minimum marks in JEE Main that students need to score. Students gets All India Rank based on the marks they secure in exam and gets admission based on that rank.

Preparation Strategy for 3D & Vectors Chapters for JEE Main 2027

Based on the recent trends in JEE Main vectors and 3D questions asked in NTA JEE Mains exam, here are some strategies that candidates should focus on while preparing for these two important chapters from the JEE Mains 2027 syllabus:

For Vectors:

  • Master the dot and cross product.
  • Focus on projection formulas
  • Practice expressing linear combinations
  • Solve the last 5 to 10 JEE Main PYQs

For 3D Geometry:

  • Memorise and derive the Shortest Distance formulas
  • Connect Vectors directly to 3D geometry
  • Practice finding the Foot of Perpendicular and Image of a Point with respect to a given line using the parametric point method.
  • Solve the last 5 to 10 JEE Main questions
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High Probability JEE Main 2027 Vector and 3D Questions

The following type of questions can appear in JEE Main 2027 exam:

Section A: Multiple Choice Questions
 
Q1. Let a = 2i + jk and b = i + 2j + k. If c is a unit vector coplanar with a and b, and perpendicular to a, then c is:
(A) 16(− i + j + k) ✔️
(B) 13(− i + jk)
(C) 16( i − 2 j + k)
(D) 12( jk)
 
Q2. The lines L1: x − 21 = y − 31 = z − 4k and L2: x − 1k = y − 42 = z − 51 are coplanar if k equals:
(A) 0 or −3
(B) 1 or −1
(C) 0 or −1 ✔️
(D) −1 or −3
 
Q3. Let the line L pass through the point (2, −1, 2) and be perpendicular to the lines r = (i + jk) + λ(2i − 2j + k) and r = (2ij + 3k) + μ(i + 2j + 2k). If the shortest distance of L from the origin is d, then d2 is:
(A) 19/9
(B) 38/9 ✔️
(C) 4/3
(D) 25/9
 
Section B: Numerical Value Questions
 
Q4. Let a, b, c be three vectors such that | a| = 3, | b| = 5, bc = 10, and the angle between b and c is π3. If a is perpendicular to b × c, then the value of |( a × b) ⋅ c| 2 is equal to _____.
A: 0
 
Q5. If the foot of the perpendicular from the point A(1, 0, 3) on the line joining the points B(4, 7, 1) and C(3, 5, 3) is (α, β, γ), then the value of α + β + γ is equal to _____.
A: 9

📄 JEE Main Previous Year Question Papers (2016 to 2026)

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Commonly asked questions
Q:   What should be the frequency of taking JEE Main mock tests?
A: 

Candidates should take JEE Main mock tests at least once a week. However, in the last month before exam, frequency should be increased to 3 to 4 mock exam per week.

Q:   What topics are mostly asked in JEE Main exam
A: 

Questions in JEE Mains exam is a blend of all the topics covered in the syllabus. However, there are some topics that are very much important and should be paid extra attentions while preparing for the exam. The list of important JEE Main topics are

Mathematics

  • 3D Geometry
  • Vector
  • Applications of Derivatives
  • Definite Integrals
  • Limit, Cnntinuity and Differentiability

Physics

  • Heat and Thermodynamics
  • Electromagnetic Waves
  • Ray & Wave Optics
  • Kinematics
  • Current Electricity
  • Magnetism

Chemistry

  • Electrochemistry
  • Chemical Kinetics
  • Thermodynamics
  • p-block elements
  • Chemical Bonding
Q:   What is Chapterwise weightage of class 11 and 12 topics in JEE Main?
A: 

Chapterwise weightage of class 11 and 12 topics in JEE Main are mentioned below:

  • Physics: Current Electricity Waves AC, Magnetism, Laws of Motion Work, Power and Energy.
  • Chemistry the high weightage topics are s and p block elements, Coordination compounds, Thermodynamics Gaseous state, Chemical bonding, Atomic structure, Polymers, Environmental Chemistry Organic Chemistry.
  • Mathematics, the high weightage topics are Sequence and Series Vectors and 3D, Integral and Differential Calculus, Definite and Indefinite Integral.
Q:   How many questions are asked in JEE Main exam?
A: 

Paper 1 has 75 questions where Physics Chemistry and Mathematics, each section has 25 questions. Out of 25 questions, 20 are MCQs and five are numerical value questions. You must answer all 5 numerical value-type questions. All 20 multiple-choice questions are compulsory. Complete all 75 questions in 3 hours.

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Commonly asked questions
Q:   From where can I get the mock test papers for the preparation of JEE Mains?
A: 

JEE Main mock tests are available online on nta.ac.in. Download these for free or you can also practice online. You can download JEE Main mock test papers for free from Shiksha page as well.

Q:   Are class 11 topics important in JEE Mains?
A: 

Yes, and in fact, in the JEE Main exam, the weightage of class 11 and topics is almost the same. Candidates have to study topics of both classes 11 and 12 with equal importance.

Q:   What type of questions are asked in JEE Main?
A: 

There are two question types in JEE Main exam. Multiple choice questions and numerical ability questions. In MCQ, every question has 4 options with only 1 correct answer. Select the correct option. In numerical ability question type, no options are there. Solve them and write answer using keyword and mouse.

Q:   Where can I get previous year JEE Main question papers?
A: 

Students can download JEE Main previous year question paper from Shiksha page. Candidates are provided JEE Main previous year question papers from the year 2014 to 2026. The papers can be downloaded as PDF and can be practised to prepare for the exam.

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I would say CSE at GFTI would be a better option if you are not sure about which branch

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Lucky

Beginner-Level 1

Answered 2 days ago

Yes, you have a great chance of getting admission to MBM University, Jaipur with a 92 percentile as a general female candidate from Rajasthan, especially if you have secured SKIT Jaipur in the mock allotment.

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Akanksha Yadav

Contributor-Level 10

Answered 2 days ago

Yes, you have a great chance of getting admission to MBM University in certain branches with a 92 percentile in JEE Main, though getting top branches like CSE may be difficult for the general category.

As you have mentioned that you got SKIT in the mock allotment, which means your rank currently alig

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Akanksha Yadav

Contributor-Level 10

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Yes, Galgotias University accepts JEE Main and CUET scores for B.Tech admissions. Students with JEE Main/JEE Advanced/CUET/SAT scores are given preference in the merit list, subject to meeting the Class 12 eligibility requirements. For B.Tech CSE, the current requirement is at least 60% in the speci

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Sanjeev yadhuvanshi

Beginner-Level 5

Answered 3 days ago

No, candidates who fulfill Babu Banarasi Das University, Lucknow BTech eligibility criteria do not need to appear in JEE Main to qualify for admission. 

However, JEE Main ranks are used to offer scholarships at BBDU, Lucknow. Thus, candidates can choose to appear in this exam for maximizing their cha

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Saurabh Khanduri

Contributor-Level 10

Answered 4 days ago

Because you have passed 12th from NIOS in year 2024. So your three consecutive years for appearing in JEE Mains are 2024, 2025 & 2026. So can't appear in year 2027 as per the eligibility criteria.

40591507
pradeep kumar

Scholar-Level 18

Answered 5 days ago

Invertis University JEE Main cutoff 2025, for all the offered BTech specialisations held the same closing rank of 145410 for round 1 under the General Home State category.

The cutoff data displayed above has been sourced from third-party channels. While we strive to ensure accuracy, cutoffs are subj

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Riya Jeet

Beginner-Level 5

Answered 5 days ago

With 98.3% in Class 12, you can easily meet the academic board criteria for IITs (65% required for ST). Since clearing JEE Advanced is mandatory for IIT admission, on the basis of JEE Main score of 56.77 percentile, you likely did not cross the ST category qualifying cutoff to appear for JEE Advance

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Akanksha Yadav

Contributor-Level 10

Answered 5 days ago

For admission in B.Planning at College of Engineering, you need to pass class 12 with Physics and Maths with at least 50% aggregate marks (45% for reserved categories and OBC candidates) from Maharashtra. Along with this, candidate is also required to qualify in either MHT CET or JEE Main and lastly

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Akanksha Yadav

Contributor-Level 10

Answered 6 days ago

NTA will release JEE Mains 2027 session 1 application form in October 2026.

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Mamona Majumder

Contributor-Level 10