Vectors — JEE Main PYQs & Practice Questions

Vectors is a Physics chapter in the JEE Main syllabus. This page brings together 42 previous-year and practice questions on Vectors, organised into 4 topics: Vector Addition and Subtraction, Dot Product, Cross Product and Resolution of Vectors. Most questions come with a step-by-step solution you can work through free in PrepWiser.

Download Vectors JEE Main PYQs as a free PDF (with answer key)

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Chapter weightage: how many questions each chapter had per shift in the 2024–26 papers.

Vector Addition and Subtraction

• Two forces F̅₁ and F̅₂ are acting on a body. One force has magnitude thrice that of the…
• Two vectors X⃗ and Y⃗ have equal magnitude. The magnitude of (X⃗ - Y⃗) is n times the…
• If two vectors A⃗ and B⃗ having equal magnitude R are inclined at angle θ, then
• When vector A⃗=2î+3ĵ+2k̂ is subtracted from vector B⃗, it gives a vector equal to 2ĵ…
• The angle between vector Q⃗ and the resultant of (2Q⃗+2P⃗) and (2Q⃗-2P⃗) is :
• Four forces are acting at a point P in equilibrium as shown in figure. The ratio of…
• A particle moves in the x-y plane with velocity v⃗ = (3î + 4ĵ) m/s. What is the…
• Statement I : Two forces (P⃗+Q⃗) and (P⃗-Q⃗) where P⃗⊥ Q⃗, when act at an angle θ₁ to…
• In an octagon ABCDEFGH of equal side, what is the sum of AB⃗+AC⃗+AD⃗+AE⃗+AF⃗+AG⃗+AH⃗…
• Two vectors A⃗ and B⃗ have equal magnitudes. If magnitude of A⃗ + B⃗ is equal to two…
• The magnitude of vectors OA⃗, OB⃗ and OC⃗ in the given figure are equal. The direction…
• Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O'…
• Which of the following relations is true for two unit vector A and B making an angle θ…
• The velocity of a particle is given as v⃗=-xî+2yĵ-zk̂ m/s. The magnitude of acceleration…
• The angle between vector (A⃗) and (A⃗-B⃗) is :
• Match List - I with List - II Choose the correct answer from the options given below :
• The sum of two forces P⃗ and Q⃗ is R⃗ such that |R⃗|=|P⃗| . The angle θ (in degrees)…
• Three vectors OP⃗,OQ⃗ and OR⃗ each of magnitude A are acting as shown in figure. The…
• Two vectors P⃗ and Q⃗ have equal magnitudes. If the magnitude of P⃗+Q⃗ is n times the…
• Two forces having magnitude A and A/2 are perpendicular to each other. The magnitude of…

Dot Product

• A force F⃗=2 î+b ĵ+k̂ is applied on a particle and it undergoes a displacement î-2 ĵ-k̂…

Cross Product

• For three vectors A⃗=(-xî-6ĵ-2k̂),B⃗=(-î+4ĵ+3k̂) and C⃗=(-8î-ĵ+3k̂), if A⃗· (B⃗× C⃗)=0…
• The torque due to the force (2 î+ĵ+2 k̂) about the origin, acting on a particle whose…
• Two particles are located at equal distance from origin. The position vectors of those…
• If A⃗ and B⃗ are two vectors satisfying the relation A⃗ . B⃗ = |A⃗× B⃗|. Then the value…
• If P⃗× Q⃗=Q⃗× P⃗, the angle between P⃗ and Q⃗ is θ(0° < θ < 360°). The value of 'θ' will…
• Three particles P, Q and R are moving along the vectors A⃗=î+ĵ, B⃗=ĵ+k̂ and C⃗=-î+ĵ…
• The torque of a force 5 î+3 ĵ-7 k̂ about the origin is τ. If the force acts on a…
• Vectors aî+bĵ+k̂ and 2î-3ĵ+4k̂ are perpendicular to each other when 3a+2b=7, the ratio…
• If a⃗ and b⃗ makes an angle cos⁻¹(5/9) with each other, then |a⃗+b⃗|=√2|a⃗-b⃗| for…
• A⃗ is a vector quantity such that |A⃗| = non-zero constant. Which of the following…
• If force F⃗ = 3î + 4ĵ - 2k̂ acts on a particle position vector 2î + ĵ + 2k̂ then, the…
• If two vectors P⃗=î+2mĵ+mk̂ and Q⃗=4î-2ĵ+mk̂ are perpendicular to each other. Then, the…
• The resultant of two vectors A⃗ and B⃗ is perpendicular to A⃗ and its magnitude is half…

Resolution of Vectors

• If P⃗=3î+√3ĵ+2k̂ and Q⃗=4î+√3ĵ+2.5k̂ then, the unit vector in the direction of P⃗× Q⃗ is…
• A mosquito is moving with a velocity v⃗ = 0.5t²î + 3tĵ + 9k̂ m/s and accelerating in…
• The resultant of these forces OP⃗,OQ⃗,OR⃗,OS⃗ and OT⃗ is approximately .......... N…
• If the projection of 2î+4ĵ-2k̂ on î+2ĵ+αk̂ is zero. Then, the value of α will be…
• What will be the projection of vector A⃗=î+ĵ+k̂ on vector B⃗=î+ĵ ?
• If A⃗=(2î+3ĵ-k̂) m and B⃗=(î+2ĵ+2k̂) m. The magnitude of component of vector A⃗ along…
• A vector in x-y plane makes an angle of 30° with y-axis. The magnitude of y-component of…

More Physics chapters

• Basic Mathematics for Physics
• Units, Dimensions & Errors
• Rectilinear Motion
• Projectile Motion & Relative Motion
• Newton's Laws of Motion
• Friction
• Circular Motion
• Work, Energy & Power
• Centre of Mass & Linear Momentum
• Collision
• Rotational Motion
• Gravitation
• Simple Harmonic Motion
• Elasticity
• Fluid Mechanics
• Surface Tension
• Thermometry & Calorimetry
• Kinetic Theory of Gases
• Thermodynamics
• Heat Transfer
• Mechanical Waves
• Sound Waves
• Experimental Skills
• Electrostatics I — Charges, Field & Gauss's Law
• Electrostatics II — Potential & Capacitance
• Current Electricity
• Moving Charges & Magnetism
• Magnetism & Matter
• Electromagnetic Induction
• Alternating Current
• Electromagnetic Waves
• Ray Optics
• Wave Optics
• Dual Nature of Radiation & Matter
• Atomic Physics
• Nuclear Physics
• Semiconductors & Electronic Devices
• Communication Systems

Frequently asked questions

How many Vectors questions are there for JEE Main?

PrepWiser has 42 Vectors questions for JEE Main, grouped into 4 topics such as Vector Addition and Subtraction, Dot Product and Cross Product.

Are these Vectors questions from previous-year JEE Main papers?

Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.

Where can I see the answers and solutions to these Vectors questions?

Open any Vectors question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.