Vector Algebra CBSE Class 12 PYQ Chapter Wise (2016–2026)

Explore: All CBSE Class 12 chapters · CBSE Class 12 Mathematics PYQs · CBSE Class 12 hub · Syllabus & pattern · Class 12 2026

Answer first

Vector Algebra PYQs (previous year questions) for CBSE Class 12: Vector Algebra (Mathematics) had 33 questions across the 50 official CBSE Class 12 papers we tagged (2016–2026), and appeared in 10 of them. Asked in 10 of 10 years. The concepts asked in the most papers: Dot Product, Cross Product, Area of Parallelogram.

Year-wise question count

Asked in 10 of 10 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Vector Algebra PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Vector Algebra questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. 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, with a link to the official PDF.

CBSE Class 122026

• Q.13 (Mathematics (65/1/1)) · MCQ · Dot Product: Value of p making two vectors perpendicular PDF
• Q.14 (Mathematics (65/1/1)) · MCQ · Collinear Vectors: Value of m for three collinear position vectors PDF
• Q.15 (Mathematics (65/1/1)) · MCQ · Dot and Cross Product: Find |a . b| from |a|, |b| and |a x b| PDF
• Q.23 (Mathematics (65/1/1)) · Very short answer · Unit Vector: Vector of magnitude 14 in the direction of QP PDF
• Q.24 (Mathematics (65/1/1)) · Very short answer · Area of Parallelogram: Diagonals of a parallelogram from two adjacent side vectors PDF

CBSE Class 122025

• Q.2 (Mathematics (65/1/1)) · MCQ · Dot Product: Which relation holds between two given vectors PDF
• Q.11 (Mathematics (65/1/1)) · MCQ · Angle Between Vectors: Angle between b and c given a + b + c = 0 and magnitudes PDF
• Q.23 (Mathematics (65/1/1)) · Very short answer · Area of Parallelogram: Area of a parallelogram from its diagonal vectors PDF
• Q.25 (Mathematics (65/1/1)) · Very short answer · Angle Between Vectors: Angle between two kite strings given as vectors PDF

CBSE Class 122024

• Q.7 (Mathematics (65/1/1)) · MCQ · Dot Product: Dot product of two unit vectors in terms of the angle between them PDF
• Q.15 (Mathematics (65/1/1)) · MCQ · Position Vectors: Vector from initial point B to terminal point A PDF
• Q.24 (Mathematics (65/1/1)) · Very short answer · Dot Product: Prove |b| = root 2 |a| from two perpendicularity conditions PDF
• Q.25 (Mathematics (65/1/1)) · Very short answer · Area of Parallelogram: Find AD and area of parallelogram from AB and DB PDF

CBSE Class 122023

• Q.8 (Mathematics (65/1/1)) · MCQ · Dot Product: Value of p making two vectors perpendicular PDF
• Q.9 (Mathematics (65/1/1)) · MCQ · Cross Product: Evaluate a combination of cross and dot products of unit vectors PDF
• Q.10 (Mathematics (65/1/1)) · MCQ · Vector Magnitude: Find |b| given a + b and a PDF
• Q.22 (Mathematics (65/1/1)) · Very short answer · Collinear Vectors: Vectors of magnitude 3 root 3 collinear with i + j + k PDF
• Q.23 (Mathematics (65/1/1)) · Very short answer · Section Formula: Express c in terms of a and b given AC relation to AB PDF

CBSE Class 122022

• Q.2 (Mathematics Term 2 (65/1/1)) · Short answer I · Vector Magnitude: Lengths of diagonals of a parallelogram from two side vectors PDF
• Q.7 (Mathematics Term 2 (65/1/1)) · Short answer II · Cross Product: Show (a - 2d) is parallel to (2b - c) from cross-product relations PDF

CBSE Class 122020

• Q.4 (Mathematics (65/1/1)) · MCQ · Projection of Vector: Find lambda so projection of a on b is zero PDF
• Q.15 (Mathematics (65/1/1)) · Fill in the blank · Section Formula: Position vector of point dividing AB in ratio 2:1 PDF
• Q.24 (Mathematics (65/1/1)) · Short answer · Cross Product: Unit vector perpendicular to two given vectors PDF

CBSE Class 122019

• Q.10 (Mathematics (65/1/1)) · Short answer · Vector Magnitude: Sum of two unit vectors is unit; prove magnitude of difference PDF
• Q.22 (Mathematics (65/1/1)) · Long answer I · Angle Between Vectors: Angle between lines AB and CD from position vectors; collinearity PDF

CBSE Class 122018

• Q.3 (Mathematics (65/1)) · Very short answer · Dot Product: Magnitudes of equal vectors given angle 60 degrees and dot product PDF
• Q.11 (Mathematics (65/1)) · Short answer · Cross Product: Find sin of angle between two given vectors PDF
• Q.20 (Mathematics (65/1)) · Long answer I · Cross Product: Vector perpendicular to two given vectors with set dot product PDF

CBSE Class 122017

• Q.19 (Mathematics (65/1)) · Long answer I · Area of Triangle: Show three position vectors form a right triangle and find area PDF
• Q.20 (Mathematics (65/1)) · Long answer I · Coplanarity: Find lambda for which four points are coplanar PDF

CBSE Class 122016

• Q.5 (Mathematics (65/1/N)) · Very short answer · Cross Product: Find lambda and mu when a cross product of two vectors is zero PDF
• Q.6 (Mathematics (65/1/N)) · Very short answer · Unit Vector: Unit vector parallel to the sum of two given vectors PDF
• Q.17 (Mathematics (65/1/N)) · Long answer I · Coplanarity: Show four given points are coplanar PDF

Other Mathematics chapters

• Relations and Functions PYQs
• Inverse Trigonometric Functions PYQs
• Matrices PYQs
• Determinants PYQs
• Continuity and Differentiability PYQs
• Application of Derivatives PYQs
• Integrals PYQs
• Application of Integrals PYQs
• Differential Equations PYQs
• Three Dimensional Geometry PYQs
• Linear Programming PYQs
• Probability PYQs

FAQ

How many Vector Algebra questions come in CBSE Class 12?

In the official papers we tagged: 5 in 2026, 4 in 2025, 4 in 2024, 5 in 2023, 2 in 2022, 3 in 2020, 2 in 2019, 3 in 2018, 2 in 2017 and 3 in 2016. That is 33 questions in all, about 10% of Mathematics.

Which Vector Algebra topics repeat in CBSE Class 12?

Asked in the most papers: Dot Product, Cross Product, Area of Parallelogram. The concept table lists every one with its count.

Are these official CBSE Class 12 questions?

Yes. Every question is from an official CBSE Class 12 paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.