JEE Main Maths · Vector Algebra

Dot Product in JEE Main

Name: Dot Product: JEE Main previous year questions
Creator: Lumi

Dot Product (Maths, Vector Algebra) came 15 times in 13 of the 42 JEE Main shifts Lumi analysed, across 12 distinct ideas. 9 of them came in 2024–26; it was last asked in 2026.

Questions: 15; in 13 shifts
Ideas asked: 12; 2 asked more than once
Numerical answer: 3; 20% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 3Medium 11Hard 1

Format

Single correct12 Q
Numerical value3 Q

Ideas inside the topic

12 ideas

Expansion of Sum of Vectors Squared3 Q
Scalar and Vector Projection2 Q
Acute and Obtuse Angle Conditions1 Q
Angle Between Vectors1 Q
Angle Bisector Construction1 Q
Dot Product Invariance Under Rotation1 Q
Orthogonality Condition1 Q
Parallelogram Law Identity1 Q
Algebraic Properties1 Q
Orthogonal Resolution of a Vector1 Q
Perpendicular Diagonals of a Rhombus1 Q
Solving Unknown Vector via Dot Products1 Q

Where it sits

Part of Vector Algebra, which had 55 questions in all. Dot Product accounts for 27% of them. In Lumi's JEE taxonomy it belongs to Vectors and 3D Geometry.

Some questions sit in other chapters too: Three Dimensional Geometry, Trigonometric Functions.

Every question

All 15 Dot Product questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q14If $\vec a$ and $\vec b$ are two vectors such that $|\vec a|=2$ and $|\vec b|=3$ , then the maximum value of…HardSingle correct
2 Apr 2026, Shift 2 · Q14Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$ . For some…MediumSingle correct
2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram $PQRS$ are given by $\vec{PQ} = \hat{j} + \hat{k}$ and $\vec{PS} = \hat{i} - \hat{j}$ . If the side…MediumSingle correct
2 Apr 2025, Shift 1 · Q11If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$ , $\hat{i}+2\hat{j}-2\hat{k}$ and…MediumSingle correct
7 Apr 2025, Shift 2 · Q15Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that…MediumSingle correct
8 Apr 2025, Shift 2 · Q14Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Let $\hat{c}$ be a unit vector in the plane of…MediumSingle correct
8 Apr 2024, Shift 1 · Q18The set of all $\alpha$ , for which the vectors $\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k}$ and…MediumSingle correct
29 Jan 2024, Shift 1 · Q18Let O be the origin and the position vectors of A and B be $2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ respectively. If…MediumSingle correct
30 Jan 2024, Shift 2 · Q18Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{b}| = 1$ and $|\vec{b} \times \vec{a}| = 2$ . Then…EasySingle correct
28 Jul 2022, Shift 1 · Q6Let a vector $\vec{a}$ has magnitude 9. Let a vector $\vec{b}$ be such that for every $(x,y)\in\mathbf{R}\times\mathbf{R}-\{(0,0)\}$ , the…MediumSingle correct
28 Jul 2022, Shift 1 · Q22Let $P(-2,-1,1)$ and $Q\left(\frac{56}{17},\frac{43}{17},\frac{111}{17}\right)$ be the vertices of the rhombus PRQS. If the direction…MediumNumerical value
29 Jun 2022, Shift 1 · Q5Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$ , $\vec{b} = 3\hat{i} - \beta\hat{j} + 4\hat{k}$ and…MediumSingle correct
18 Mar 2021, Shift 1 · Q80A vector $\vec{a}$ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle…MediumSingle correct
2 Sep 2020, Shift 1 · Q75Let $\vec{a}$ , $\vec{b}$ and $\vec{c}$ be three unit vectors such that $|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8$ . Then…EasyNumerical value
6 Sep 2020, Shift 2 · Q74If $\vec{x}$ and $\vec{y}$ be two non-zero vectors such that $|\vec{x}+\vec{y}|=|\vec{x}|$ and $2\vec{x}+\lambda\vec{y}$ is perpendicular…EasyNumerical value