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JEE Advanced Vector Algebra questions with solutions

Dot and cross products and vector geometry. 9 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Vector Algebra for JEE Main · Vector Algebra for NDA

JEE Advanced 2025

Let vec a=hat i+2hat j-hat k, vec b=2hat i-hat j+hat k and vec c=hat i+2hat j+3hat k. A vector vec r satisfies vec r×vec a=vec b×vec a and vec r·vec…JEE Advanced 2025 Paper 2 · medium

JEE Advanced 2024

Let vec a=hat i+2hat j+2hat k, vec b=2hat i+hat j-2hat k, vec c=2hat i-hat j+3hat k. Match the entries of List-I with List-II. List-I P. |vec a×vec…JEE Advanced 2024 Paper 1 · medium
Let vec a,vec b be unit vectors with angle (π)/(3) between them, and let vec c=2(vec a×vec b)+3vec a-vec b. The value of 4 [vec a vec b vec c]^2 isJEE Advanced 2024 Paper 2 · easy

JEE Advanced 2023

Let vec a=hat i+2hat j+2hat k, vec b=2hat i+hat j-2hat k and vec c=hat i+hat j+hat k. A vector vec r satisfies vec r×vec a=vec b and vec r·vec c=3.…JEE Advanced 2023 Paper 1 · medium
Let vec u,vec v,vec w be unit vectors such that the angle between every two of them is 60^°. The volume of the parallelepiped whose coterminous edges…JEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

Let vec a=hat i+2hat j-hat k, vec b=2hat i-hat j+hat k, vec c=hat i+hat j+3hat k.JEE Advanced 2022 Paper 1 · medium

JEE Advanced 2020

Points A(1,0,2), B(3,1,0) and C(2,3,1) are given. The perpendicular distance of the point D(2,4,5) from the plane ABC is d. Find d.JEE Advanced 2020 Paper 1 · medium

JEE Advanced 2019

Let vec a,vec b,vec c be unit vectors such that vec a·vec b=vec b·vec c=vec c·vec a=1/2. The volume of the parallelepiped whose coterminous edges are…JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2016

Let vec a,vec b,vec c be unit vectors such that the angle between each pair is (π)/(3). If vec d=vec a×vec b+vec b×vec c+vec c×vec a, then the value…JEE Advanced 2016 Paper 1 · hard

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18