JEE Main Maths · Vector Algebra PYQ

JEE Main Vector Algebra PYQ (2002–2025)

Vector Algebra is a P1 chapter — ~5% JEE Main weightage with 1–2 questions per session. It's the foundation for 3D Geometry and the physics chapters that use vectors (Mechanics, EMI). Mastery here unlocks both chapters at once.

Vector Algebra PYQs from 2002 to 2025, tagged by sub-topic (dot product, cross product, triple products, projections). Every KaTeX solution shows the vector decomposition and applies the appropriate formula.

Practise Vector Algebra PYQs All Maths PYQs

Vector Algebra at a Glance

Weightage

~5%

approx · 10-yr avg

Priority

Must master

Year range

2002–2025

PYQ coverage

Typical in paper

1–2

per session

Key Sub-Topics & What's Tested

Vector Basics

Position vector, unit vector, collinear vectors, coplanar vectors, vector addition (parallelogram/triangle law).

Dot Product (Scalar Product)

a·b = |a||b|cos θ, properties (commutative, distributive), a·a = |a|², perpendicular vectors a·b = 0.

Cross Product (Vector Product)

a × b = |a||b|sin θ n̂, anti-commutative, area of parallelogram = |a × b|, area of triangle = ½|a × b|.

Projection of Vector

Projection of a on b = (a·b)/|b|, vector projection, decomposition into parallel and perpendicular components.

Scalar Triple Product

[a b c] = a · (b × c), volume of parallelepiped, coplanarity condition [a b c] = 0, determinant form.

Vector Triple Product

a × (b × c) = (a·c)b - (a·b)c, BAC-CAB rule, applications in deriving identities.

Angles Between Vectors

cos θ = (a·b)/(|a||b|), sin θ = |a × b|/(|a||b|), using Cartesian components.

Coplanarity & Collinearity

Three vectors coplanar iff [a b c] = 0. Three points collinear iff vectors between them are parallel.

Question Type Distribution

Question Type	Share (approx)	Example Pattern
Dot Product Application	20%	Find angle between vectors a = 2i + 3j - k and b = i - j + 2k.
Cross Product / Area	20%	Find area of triangle with vertices A(1,2,3), B(2,3,4), C(3,4,5).
Scalar Triple / Volume	20%	Find volume of parallelepiped formed by vectors a, b, c given as 3-component vectors.
Projection Problems	15%	Find projection of vector a = 3i + 4j onto b = i + j.
Coplanarity Check	15%	Determine if vectors (1,0,1), (2,1,3), (3,1,4) are coplanar.
Vector Triple / Identity	10%	Simplify a × (b × c) + b × (c × a) + c × (a × b).

How to Solve Vector Algebra PYQs

1
Dot product computes angles and projections. a·b = 0 → perpendicular. a·b > 0 → acute angle. a·b < 0 → obtuse. Basic but crucial.
2
Cross product for area and perpendicular direction. |a × b| = area of parallelogram. a × b is perpendicular to both a and b. Never forget the perpendicular property.
3
Scalar triple product = volume. [a b c] > 0 → right-handed system. [a b c] = 0 → coplanar vectors.
4
Use Cartesian components for computation. Express vectors as (x, y, z) triples. Then compute dot/cross products via formulas in terms of components.
5
BAC-CAB rule for vector triple product. a × (b × c) = b(a·c) - c(a·b) — memorise this one formula.

Common Mistakes That Cost Marks

Wrong direction in cross product. a × b follows right-hand rule. a × b ≠ b × a; in fact, a × b = -b × a. Sign matters.
Confusing dot and cross products in formulas. Dot product gives scalar. Cross product gives vector. Mixing these breaks dimensional analysis.
Calling |a × b| the area of triangle. |a × b| is area of PARALLELOGRAM formed by a and b. Triangle area = half of that.
Using |a| · |b| as projection. Projection of a on b = (a·b)/|b|. The scalar product is divided by the magnitude of b, not multiplied.
Computing scalar triple as dot of triples. [a b c] = a · (b × c). NOT (a · b) · c — that doesn't make sense dimensionally.

JEE Main Maths PYQ Chapter-Wise

Browse PYQs across all Maths chapters.

JEE Main 3D Geometry PYQ

Uses vectors extensively — direct downstream application.

JEE Main Complex Numbers PYQ

Algebra companion — parallel concepts in 2D.

Top High-Weightage Maths Chapters (data-backed)

Where Vectors sits in the priority order.

JEE Main Maths Syllabus with Priority Tiers

Full Maths syllabus with priority tiers.

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Frequently asked questions

How many Vectors PYQs should I solve?

Target 50–70 PYQs across 2010–2025. Given the chapter's cross-use in 3D Geometry and Physics, consistent practice has compound value.

Are Vectors questions computation-heavy or conceptual?

Both. ~60% computation (dot/cross products, triple products). ~40% conceptual (coplanarity, projection, geometric interpretation). Balance both types in practice.

Do I need to know vector identities by heart?

Core ones: BAC-CAB, scalar triple as determinant, a × (b × c) ≠ (a × b) × c (non-associative). These appear in derivation-type PYQs.

What's the most-tested Vectors PYQ pattern?

Coplanarity of three vectors via scalar triple product = 0. Appears in 3–4 PYQs per 10-year window. Master the determinant setup.

Do I need to know projection vs rejection separately?

Projection of a on b = (a·b/|b|²) b (vector). Rejection = a - projection. Most PYQs ask for projection (vector) or projection component (scalar). Know both terminologies.

How does Vectors connect with 3D Geometry?

3D Geometry uses vectors throughout — line equations, plane equations, shortest distance, angle between lines. Strong Vectors fluency directly helps 3D PYQs.

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