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JEE Main Vector Algebra questions with solutions

Dot and cross products and vector geometry. 8 questions from our 2016–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

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

JEE Main 2025

Let vec a=hat i+hat j and vec b=hat j+hat k. The magnitude of the scalar projection of vec p=2hat i+3hat j+5hat k on a vector perpendicular to both…JEE Main 2025 · medium

JEE Main 2024

Let vec a=hat i+hat j+hat k and let vec b be a vector with vec a×vec b=hat j-hat k and vec a·vec b=3. Then vec b·(hat i-hat j) equalsJEE Main 2024 · hard

JEE Main 2023

The projection of vec a=hat i+2hat j+2hat k on vec b=2hat i-hat j+2hat k isJEE Main 2023 · easy

JEE Main 2021

If vec a,vec b are vectors with |vec a|=2, |vec b|=3 and vec a·vec b=3, then |vec a×vec b| equalsJEE Main 2021 · medium

JEE Main 2020

Let vec a,vec b be unit vectors inclined at an angle of 60^°. The volume of the parallelepiped whose coterminous edges are vec a, vec b and vec a×vec…JEE Main 2020 · medium

JEE Main 2019

A parallelogram is formed with vec a=hat i+2hat j+3hat k and vec b=2hat i-hat j+hat k as two adjacent sides. Its area isJEE Main 2019 · medium

JEE Main 2017

If vec a=hat i+2hat j+3hat k and vec b=2hat i-hat j+hat k, then |vec a×vec b| equalsJEE Main 2017 · medium

JEE Main 2016

The area of the triangle with adjacent sides vec a=hat i+2hat j-hat k and vec b=2hat i-hat j+hat k isJEE Main 2016 · medium

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Differentiation and Application of Derivatives 19 Indefinite and Definite Integrals 16 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Probability 9 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9