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

JEE Main 2027 Exam Date Session 1

22 Jan '27 - 24 Jan '27

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 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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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).

Also Check: JEE Main 2027 Matrices & Determinants Questions

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.

Download JEE Mains 2027 Vector Questions PDF

Download JEE Mains 2027 3D Questions PDF

Q1. Let O be the origin. Let OP = x i + y j − k 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( 1√3)

(2) sin ⁻¹( 1√6)

(3) cos ⁻¹( 1√3)

(4) cos ⁻¹( 1√2)

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 | a − b| ² + | b − c| ² + | c − a| 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 = z − ac and L ₂ : x − 1b = y − 23 = z − a4 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

Commonly asked questions

Q: Is there negative marking in JEE Main?

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

Q: Which mock tests are best for JEE Mains?

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?

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?

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 + j − k and b = i + 2j + k. If c is a unit vector coplanar with a and b, and perpendicular to a, then c is:

(A) 1√6(− i + j + k) ✔️

(B) 1√3(− i + j − k)

(D) 1√2( j − k)

Q2. The lines L₁: x − 21 = y − 31 = z − 4−k and L₂: x − 1k = y − 42 = z − 51 are coplanar if k equals:

(A) 0 or −3

(B) 1 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 + j − k) + λ(2i − 2j + k) and r = (2i − j + 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 ✔️

(D) 25/9

Section B: Numerical Value Questions

Q4. Let a, b, c be three vectors such that | a| = √3, | b| = 5, b ⋅ c = 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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📅 JEE Main 2021 to 2016

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Commonly asked questions

Q: What should be the frequency of taking JEE Main mock tests?

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

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?

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?

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.

Commonly asked questions

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

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?

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?

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?

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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