JEE Main Maths · Vector Algebra

Simultaneous Cross and Dot Equations

Simultaneous Cross and Dot Equations (Vector Algebra) was asked 3 times in 3 JEE Main shifts, 2024–2025, out of the 42 shifts Lumi analysed. 2 of the 3 had a numerical answer.

Times asked: 3; in 3 shifts
Years: 2024–2025
Usual format: Numerical value; Multi-step
Pattern: New since 2024; repeats across shifts

How it is asked

Unknown vector from cross and dot conditions
Vector from cross and dot conditions

Difficulty

Easy 0Medium 2Hard 1

Where it sits

Chapter: Vector Algebra. Topic: Cross Product, 32 questions over 11 ideas.

All 3 questions

Newest first, each with its options and official answer.

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 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
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