Explore: All NDA topics · NDA Mathematics PYQs · NDA hub · Syllabus & pattern · NDA 2026
Answer first
Vector Algebra PYQs (previous year questions) for NDA: Vector Algebra (Mathematics) had 111 questions across the 42 official NDA papers we tagged (2016–2026), and appeared in 21 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Dot Product, Cross Product, Vector Products.
Year-wise question count
Asked in 11 of 11 years.
| Year | Papers | Questions | Per paper |
|---|---|---|---|
| NDA 2026 | 2 | 11 | 5.5 |
| NDA 2025 | 2 | 10 | 5 |
| NDA 2024 | 2 | 10 | 5 |
| NDA 2023 | 2 | 11 | 5.5 |
| NDA 2022 | 2 | 10 | 5 |
| NDA 2021 | 2 | 10 | 5 |
| NDA 2020 | 1 | 5 | 5 |
| NDA 2019 | 2 | 10 | 5 |
| NDA 2018 | 2 | 13 | 6.5 |
| NDA 2017 | 2 | 10 | 5 |
| NDA 2016 | 2 | 11 | 5.5 |
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Dot Product | 24 | 15 | 2026, 2025, 2024, 2022, 2020, 2019, 2018, 2017, 2016 |
| Cross Product | 19 | 12 | 2025, 2024, 2020, 2019, 2018, 2017, 2016 |
| Vector Products | 14 | 6 | 2026, 2023, 2022 |
| Position Vectors | 7 | 6 | 2023, 2022, 2020, 2019, 2018, 2016 |
| Moment of Force | 5 | 5 | 2025, 2024, 2018, 2016 |
| Vector Addition | 8 | 4 | 2024, 2022, 2018, 2017 |
| Angle Between Vectors | 4 | 3 | 2018, 2016 |
| Vector Triple Product | 3 | 3 | 2025, 2024, 2021 |
| Dot and Cross Product | 6 | 2 | 2021 |
| Collinear Vectors | 2 | 2 | 2023, 2022 |
| Coplanar Vectors | 2 | 2 | 2017 |
| Scalar Triple Product | 2 | 2 | 2021, 2020 |
| Unit Vectors | 2 | 2 | 2020, 2019 |
| Vector Basics | 2 | 2 | 2021 |
| Direction Cosines | 2 | 1 | 2023 |
| Scalar Product | 2 | 1 | 2023 |
| Vector Components | 2 | 1 | 2016 |
| Direction Angles | 1 | 1 | 2024 |
| Section Formula | 1 | 1 | 2025 |
| Vector Identities | 1 | 1 | 2019 |
| Vector Operations | 1 | 1 | 2019 |
| Work Done | 1 | 1 | 2017 |
How to practise Vector Algebra PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Vector Algebra questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.
NDA2026
- Q.65 (NDA (I) Mathematics) · MCQ · Dot Product: Angle between vectors a and b from unit-vector conditions PDF
- Q.66 (NDA (I) Mathematics) · MCQ · Dot Product: Angle between vectors a and c from the same conditions PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Vector Products: Orthogonality and unit-length statements for three vectors PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Vector Products: Statements on scalar and vector triple products PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Vector Products: Value of p+q when c is written in a, b and a×b PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Vector Products: Value of r² in the same expansion of c PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Vector Products: Count of ill-defined dot/cross product expressions PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Dot Product: Value of λ from a scalar projection PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Dot Product: Angle of a vector with the positive z-axis PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Vector Products: Area of a parallelogram with given vector sides PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Vector Products: Express a vector via b × c given angle conditions PDF
NDA2025
- Q.66 (NDA (I) Mathematics) · MCQ · Dot Product: Dot product of a vector of squared direction sines with i+j+k PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Vector Triple Product: Statements on coplanarity and perpendicularity of (a×b)×c PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Section Formula: Ratio AB:BC when 3a-4b+c=0 for position vectors PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Cross Product: Sum of cyclic cross products for collinear-type position vectors PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Cross Product: a·b when a, b and a×b are all unit vectors PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Cross Product: |p×q| for p=a-b, q=a+b with given magnitudes PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Cross Product: Which vectors are perpendicular to two given vectors PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Cross Product: Area of a parallelogram from two side vectors PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Dot Product: Angle between diagonals of a quadrilateral from position vectors PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Moment of Force: λ from the moment of a force about a point PDF
NDA2024
- Q.66 (NDA (I) Mathematics) · MCQ · Vector Triple Product: α+β+γ from a vector triple product PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Direction Angles: Components of a vector given its angles with the axes PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Moment of Force: Statements about moment of a force about a point and a line PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Cross Product: Simplify a sum of cross products with unit vectors PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Dot Product: Angle between a and a-b for equal-magnitude vectors PDF
- Q.51 (NDA (II) Mathematics) · MCQ · Cross Product: 3α+2β when a cross product is the null vector PDF
- Q.52 (NDA (II) Mathematics) · MCQ · Dot Product: Angle maximising |a×b|+√3|a·b| PDF
- Q.53 (NDA (II) Mathematics) · MCQ · Dot Product: cosθ+cos2θ for perpendicular combinations of unit vectors PDF
- Q.54 (NDA (II) Mathematics) · MCQ · Vector Addition: mn for vector relations in a regular hexagon PDF
- Q.55 (NDA (II) Mathematics) · MCQ · Dot Product: Possible vector c making equal angles with a and b PDF
NDA2023
- Q.65 (NDA (I) Mathematics) · MCQ · Vector Products: Find vector b from given dot and cross products (official answer: B) PDF
- Q.66 (NDA (I) Mathematics) · MCQ · Vector Products: Angle between a + b and a given vector (official answer: A) PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Direction Cosines: cos α for the angle a vector makes with the x-axis (official answer: B) PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Direction Cosines: Value of cos 2β + cos 2γ for the vector (official answer: A) PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Position Vectors: Which points lie on the line joining A and B (official answer: B) PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Position Vectors: Magnitude of vector AB from position vectors (official answer: C) PDF
- Q.91 (NDA (II) Mathematics) · MCQ · Scalar Product: Length of projection of one vector on another (official answer: B) PDF
- Q.92 (NDA (II) Mathematics) · MCQ · Vector Products: Find |a| from (a × b)^2 + (a · b)^2 and |b| (official answer: A) PDF
- Q.93 (NDA (II) Mathematics) · MCQ · Scalar Product: Range of angle between vectors with a given dot product condition (official answer: C) PDF
- Q.94 (NDA (II) Mathematics) · MCQ · Collinear Vectors: Value of β making given vectors collinear (official answer: C) PDF
- Q.95 (NDA (II) Mathematics) · MCQ · Vector Products: Unit vectors perpendicular to two vectors and their angle (official answer: B) PDF
NDA2022
- Q.96 (NDA (I) Mathematics) · MCQ · Collinear Vectors: Values of p and q for two collinear vectors (official answer: C) PDF
- Q.97 (NDA (I) Mathematics) · MCQ · Position Vectors: Vector AG from position vectors of a triangle and its centroid (official answer: C) PDF
- Q.98 (NDA (I) Mathematics) · MCQ · Vector Products: Distributive and associative properties of dot and cross products (official answer: C) PDF
- Q.99 (NDA (I) Mathematics) · MCQ · Vector Products: Uniqueness of a vector in a cross product equation (official answer: B) PDF
- Q.100 (NDA (I) Mathematics) · MCQ · Dot Product: Range of an angle when the difference of unit vectors is bounded (official answer: D) PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Vector Addition: Side of a parallelogram from its diagonal vectors (official answer: D) PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Dot Product: Angle between unit vectors from a perpendicularity condition (official answer: C) PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Vector Products: Value of a product of coplanar unit vectors (official answer: D) PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Dot Product: Values of x making the angle between two vectors obtuse (official answer: A) PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Dot Product: Angle C of a triangle from position vectors (official answer: D) PDF
NDA2021
- Q.71 (NDA (I) Mathematics) · MCQ · Vector Basics: Components of a vector equally inclined to axes with magnitude 2 (official answer: C) PDF
- Q.72 (NDA (I) Mathematics) · MCQ · Dot and Cross Product: Perpendicularity of a+b with a-b and a x b (official answer: B) PDF
- Q.73 (NDA (I) Mathematics) · MCQ · Dot and Cross Product: Implication of equal magnitudes of a+b and a-b (official answer: C) PDF
- Q.74 (NDA (I) Mathematics) · MCQ · Scalar Triple Product: Value of a triple-product expression for coplanar vectors (official answer: C) PDF
- Q.75 (NDA (I) Mathematics) · MCQ · Dot and Cross Product: Statements on products and sums of unit vectors (official answer: D) PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Dot and Cross Product: Statements for unit vectors with a x b perpendicular to c (official answer: B) PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Dot and Cross Product: Angle between a and b from two linear combinations (official answer: D) PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Dot and Cross Product: Value of (a+b).b with perpendicularity and magnitude (official answer: A) PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Vector Triple Product: Properties of (a x b) x c for coplanar vectors (official answer: C) PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Vector Basics: Magnitude of AB from position vectors (official answer: C) PDF
NDA2020
- Q.66 (NDA (I & II) Mathematics) · MCQ · Unit Vectors: Unit vector in xy-plane at 30° to x-axis (official answer: A) PDF
- Q.67 (NDA (I & II) Mathematics) · MCQ · Position Vectors: Vector OA from its length and two direction angles (official answer: C) PDF
- Q.68 (NDA (I & II) Mathematics) · MCQ · Dot Product: Dot product of diagonals of a parallelogram (official answer: C) PDF
- Q.69 (NDA (I & II) Mathematics) · MCQ · Cross Product: |b| from Lagrange's identity (official answer: A) PDF
- Q.70 (NDA (I & II) Mathematics) · MCQ · Scalar Triple Product: p for three coplanar vectors (official answer: B) PDF
NDA2019
- Q.66 (NDA (I) Mathematics) · MCQ · Dot Product: Value of (b - a)·(3a + b) for given vectors (official answer: B) PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Position Vectors: Length of AB from position vectors (official answer: D) PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Dot Product: Sum of dot products in a right-angled triangle (official answer: A) PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Cross Product: Sine of the angle between two vectors (official answer: B) PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Dot Product: λ for which two vectors are perpendicular (official answer: D) PDF
- Q.46 (NDA (II) Mathematics) · MCQ · Dot Product: Scalar projection of one vector on another (official answer: B) PDF
- Q.47 (NDA (II) Mathematics) · MCQ · Vector Operations: Vectors with equal magnitudes of sum and difference (official answer: B) PDF
- Q.48 (NDA (II) Mathematics) · MCQ · Vector Identities: Which vector identities hold (official answer: C) PDF
- Q.49 (NDA (II) Mathematics) · MCQ · Cross Product: Statements on magnitude and zero cross product (official answer: B) PDF
- Q.50 (NDA (II) Mathematics) · MCQ · Unit Vectors: sin²(θ/2) for unit vectors in terms of |a - b| (official answer: B) PDF
NDA2018
- Q.66 (NDA (I) Mathematics) · MCQ · Angle Between Vectors: Acute angle between vectors from magnitudes and product (official answer: A) PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Position Vectors: Condition when OR ⊥ OS for division points (official answer: A) PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Moment of Force: Moment of a force about a point (official answer: A) PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Cross Product: Value of λ from a+2b+3c=0 and cross products (official answer: D) PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Cross Product: Cross product of parallel vectors (official answer: B) PDF
- Q.63 (NDA (II) Mathematics) · MCQ · Vector Addition: Condition for |a+b|=|a|+|b| (official answer: D) PDF
- Q.64 (NDA (II) Mathematics) · MCQ · Dot Product: Value of r·(i+j+k) (official answer: D) PDF
- Q.65 (NDA (II) Mathematics) · MCQ · Cross Product: Unit vector perpendicular to two vectors (official answer: A) PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Vector Addition: |a+b| given |a|, |b| and |a−b| (official answer: D) PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Vector Addition: Magnitudes of sums of mutually perpendicular unit vectors (official answer: C) PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Cross Product: Value of (a−b)×(a+b) (official answer: C) PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Moment of Force: Moment on a spacecraft from a force along k (official answer: C) PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Vector Addition: Correct vector statements for triangle sides (official answer: A) PDF
NDA2017
- Q.66 (NDA (I) Mathematics) · MCQ · Coplanar Vectors: m and n for coplanar vectors with given magnitude (official answer: D) PDF
- Q.67 (NDA (I) Mathematics) · MCQ · Vector Addition: OA+OB+OC+OD for a parallelogram (official answer: B) PDF
- Q.68 (NDA (I) Mathematics) · MCQ · Vector Addition: Correct vector relation in a quadrilateral (official answer: B) PDF
- Q.69 (NDA (I) Mathematics) · MCQ · Cross Product: Conclusion from a×b=c and b×c=a (official answer: A) PDF
- Q.70 (NDA (I) Mathematics) · MCQ · Dot Product: Value of λ for perpendicular vectors (official answer: B) PDF
- Q.45 (NDA (II) Mathematics) · MCQ · Dot Product: Magnitude of a vector perpendicular to two vectors (official answer: B) PDF
- Q.46 (NDA (II) Mathematics) · MCQ · Cross Product: Direction of (a+b)×(a−b) for unit vectors (official answer: A) PDF
- Q.47 (NDA (II) Mathematics) · MCQ · Work Done: Work done by a force over a displacement (official answer: C) PDF
- Q.48 (NDA (II) Mathematics) · MCQ · Cross Product: Sum of |a×i|²+|a×j|²+|a×k|² (official answer: B) PDF
- Q.51 (NDA (II) Mathematics) · MCQ · Coplanar Vectors: Sum of 1/(1−a) terms for coplanar vectors (official answer: B) PDF
NDA2016
- Q.74 (NDA (I) Mathematics) · MCQ · Angle Between Vectors: cos(θ/2) for angle θ between two unit vectors (official answer: B) PDF
- Q.75 (NDA (I) Mathematics) · MCQ · Angle Between Vectors: sin(θ/2) or related expression for two unit vectors (official answer: A) PDF
- Q.110 (NDA (I) Mathematics) · MCQ · Cross Product: Unit vector orthogonal to two given vectors (official answer: B) PDF
- Q.111 (NDA (I) Mathematics) · MCQ · Position Vectors: Position vectors of an equilateral triangle with orthocentre at origin (official answer: A) PDF
- Q.112 (NDA (I) Mathematics) · MCQ · Cross Product: Area of parallelogram from its diagonal vectors (official answer: C) PDF
- Q.65 (NDA (II) Mathematics) · MCQ · Vector Components: Component of a vector parallel to another (official answer: A) PDF
- Q.66 (NDA (II) Mathematics) · MCQ · Vector Components: Equations satisfied by the perpendicular component (official answer: D) PDF
- Q.67 (NDA (II) Mathematics) · MCQ · Dot Product: Sum a·b+b·c+c·a for vectors summing to zero (official answer: B) PDF
- Q.68 (NDA (II) Mathematics) · MCQ · Angle Between Vectors: Angle between a and b for vectors summing to zero (official answer: C) PDF
- Q.69 (NDA (II) Mathematics) · MCQ · Dot Product: Sum of dot products of sides in a right triangle (official answer: B) PDF
- Q.70 (NDA (II) Mathematics) · MCQ · Moment of Force: Moment of a force about a point (official answer: C) PDF
Other Mathematics topics
- Algebra PYQs
- Matrices and Determinants PYQs
- Trigonometry PYQs
- Analytical Geometry (2D and 3D) PYQs
- Differential Calculus PYQs
- Integral Calculus and Differential Equations PYQs
- Statistics and Probability PYQs
FAQ
How many Vector Algebra questions come in NDA?
In the official papers we tagged: 11 in 2026 (2 papers), 10 in 2025 (2 papers), 10 in 2024 (2 papers), 11 in 2023 (2 papers), 10 in 2022 (2 papers), 10 in 2021 (2 papers), 5 in 2020 (1 paper), 10 in 2019 (2 papers), 13 in 2018 (2 papers), 10 in 2017 (2 papers) and 11 in 2016 (2 papers). That is 111 questions in all, about 4% of Mathematics.
Which Vector Algebra topics repeat in NDA?
Asked in the most papers: Dot Product, Cross Product, Vector Products. The concept table lists every one with its count.
Are these official NDA questions?
Yes. Every question is from an official NDA paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.