JEE Main Maths · Vector Algebra

Cross Product in JEE Main

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

Cross Product (Maths, Vector Algebra) came 32 times in 28 of the 42 JEE Main shifts Lumi analysed, across 11 distinct ideas. 20 of them came in 2024–26; it was last asked in 2026.

Questions: 32; in 28 shifts
Ideas asked: 11; 6 asked more than once
Numerical answer: 9; 28% 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 2Medium 20Hard 10

Format

Single correct21 Q
Numerical value9 Q
Two statements2 Q

Ideas inside the topic

11 ideas

Solving Vector Equations with Cross Products8 Q
Magnitude and Sine Formula6 Q
Area of Triangles and Parallelograms4 Q
Area of Quadrilateral via Diagonals3 Q
Lagrange's Identity3 Q
Simultaneous Cross and Dot Equations3 Q
Condition for Parallel Vectors1 Q
Determinant Calculation Method1 Q
Orthogonality Dot Product Trap1 Q
Anti-commutativity and Distributivity1 Q
Unit Normal Vector Calculation1 Q

Where it sits

Part of Vector Algebra, which had 55 questions in all. Cross Product accounts for 58% of them. In Lumi's JEE taxonomy it belongs to Vectors and 3D Geometry.

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

Every question

All 32 Cross Product questions

Newest first, each with its options and official answer.

4 Apr 2026, Shift 2 · Q15Let $\hat u$ and $\hat v$ be unit vectors inclined at an acute angle such that $|\hat u\times\hat v|=\frac{\sqrt3}{2}$ . If…HardSingle correct
5 Apr 2026, Shift 1 · Q14Let $\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + 2\hat{k}$ . If $\vec{r}$ is a vector such that…MediumSingle correct
6 Apr 2026, Shift 1 · Q23If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ , $\vec{b}=\hat{j}-\hat{k}$ and $\vec{c}$ be three vectors such that $\vec{a}\times\vec{c}=\vec{b}$ …MediumNumerical value
6 Apr 2026, Shift 2 · Q15Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$ . Then the square of the area of the triangle with…EasySingle correct
8 Apr 2026, Shift 2 · Q14Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$ , $\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}$ and a vector $\vec{c}$ be such that…MediumSingle correct
2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…MediumSingle correct
2 Apr 2025, Shift 2 · Q16Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ , $\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k}$ and a vector $\vec{c}$ be such that…MediumSingle correct
3 Apr 2025, Shift 1 · Q24Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 3\hat{i} + 2\hat{j} - \hat{k}, \vec{c} = \lambda\hat{j} + \mu\hat{k}$ and $\hat{d}$ …MediumNumerical value
3 Apr 2025, Shift 2 · Q24Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k}, \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k}$ and…MediumNumerical value
7 Apr 2025, Shift 1 · Q15Let the angle $\theta$ , $0 < \theta < \frac{\pi}{2}$ between two unit vectors $\hat{a}$ and $\hat{b}$ be…MediumSingle correct
6 Apr 2024, Shift 2 · Q19Let $\vec{a}=6\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . If $\vec{c}$ is a vector such that $|\vec{c}|\ge 6$ ,…HardSingle correct
8 Apr 2024, Shift 1 · Q28Let $\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}$ , $\vec{b}=3\hat{i}+7\hat{j}-13\hat{k}$ and $\vec{c}=17\hat{i}-2\hat{j}+\hat{k}$ be three given…HardNumerical value
9 Apr 2024, Shift 1 · Q17Let $\overrightarrow{OA}=2\vec{a}$ , $\overrightarrow{OB}=6\vec{a}+5\vec{b}$ and $\overrightarrow{OC}=3\vec{b}$ , where O is the origin. If…MediumSingle correct
9 Apr 2024, Shift 1 · Q18Let three vectors $\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}$ , $\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}$ , $\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}$ …MediumSingle correct
9 Apr 2024, Shift 2 · Q17Between the following two statements: Statement I : Let $\vec{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-\hat{k}$ . Then…HardTwo statements
9 Apr 2024, Shift 2 · Q18Let $\vec{a}=2\hat{i}+\alpha\hat{j}+\hat{k},\ \vec{b}=-\hat{i}+\hat{k},\ \vec{c}=\beta\hat{j}-\hat{k}$ , where $\alpha$ and $\beta$ are…MediumSingle correct
30 Jan 2024, Shift 2 · Q19Let $\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}$ , $\alpha, \beta \in \mathbb{R}$ . Let a vector $\vec{b}$ be such that the angle…MediumSingle correct
31 Jan 2024, Shift 1 · Q18Let $\vec{a}=3\hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=4\hat{i}+\hat{j}+7\hat{k}$ and $\vec{c}=\hat{i}-3\hat{j}+4\hat{k}$ be three vectors. If…MediumSingle correct
31 Jan 2024, Shift 1 · Q30Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,\ |\vec{b}|=4$ , and $\vec{a}\cdot\vec{b}=2$ . If…MediumNumerical value
31 Jan 2024, Shift 2 · Q30Let $\vec{a}=3\hat{i}+2\hat{j}+\hat{k}$ , $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}$ be a vector such that…HardNumerical value
6 Apr 2023, Shift 1 · Q16Let $\vec a=2\hat i+3\hat j+4\hat k$ , $\vec b=\hat i-2\hat j-2\hat k$ and $\vec c=-\hat i+4\hat j+3\hat k$ . If $\vec d$ is a vector…MediumSingle correct
8 Apr 2023, Shift 2 · Q15The area of the quadrilateral $ABCD$ with vertices $A(2, 1, 1)$ , $B(1, 2, 5)$ , $C(-2, -3, 5)$ and $D(1, -6, -7)$ is equal toMediumSingle correct
11 Apr 2023, Shift 1 · Q11Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\ \hat{i}+\hat{k}$ …HardSingle correct
13 Apr 2023, Shift 2 · Q17Let $|\vec{a}|=2$ , $|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$ . Then…MediumSingle correct
13 Apr 2023, Shift 2 · Q18Let for a triangle ABC, $\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}$ $\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ …MediumSingle correct
25 Jul 2022, Shift 1 · Q15Let $ABC$ be a triangle such that $\overrightarrow{BC}=\vec a$ , $\overrightarrow{CA}=\vec b$ , $\overrightarrow{AB}=\vec c$ ,…HardTwo statements
24 Jun 2022, Shift 1 · Q16Let $\hat{a}, \hat{b}$ be unit vectors. If $\vec{c}$ be a vector such that the angle between $\hat{a}$ and $\vec{c}$ is $\frac{\pi}{12}$ ,…HardSingle correct
3 Aug 2021, Shift 2 · Q90Let $\vec{a} = 2\hat{i} + \alpha\hat{j} + \hat{k}$ and $\vec{b} = \beta\hat{i} - 5\hat{j} + \gamma\hat{k}$ , where $\alpha$ , $\beta$ and…MediumNumerical value
25 Jul 2021, Shift 1 · Q82Let $\vec{p}=2\hat{i}+3\hat{j}+\hat{k}$ and $\vec{q}=\hat{i}+2\hat{j}+\hat{k}$ be two vectors. If a vector…EasyNumerical value
16 Mar 2021, Shift 2 · Q63Let $\vec a=\hat i+2\hat j-3\hat k$ and $\vec b=2\hat i-3\hat j+5\hat k$ . If $\vec r\times\vec a=\vec b\times\vec r$ ,…HardSingle correct
9 Jan 2020, Shift 2 · Q75Let $\vec{a}$ , $\vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}|=\sqrt3$ , $|\vec{b}|=5$ , $\vec{b}\cdot\vec{c}=10$ and the…MediumNumerical value
2 Apr 2017 (offline) · Q84Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . Let $\vec{c}$ be a vector such that $|\vec{c}-\vec{a}|=3$ ,…HardSingle correct