JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q24

Question 24 of 75 in this shift, Maths question 24 of 25, Section B.

Let

\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

\vec{d}

be a vector such that

\vec{b} \times \vec{d} = \vec{c} \times \vec{d}

and

\vec{a} \cdot \vec{d} = 4

. Then

\left|(\vec{a} \times \vec{d})\right|^2

is equal to ________.

Official answer

128

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Simultaneous Cross and Dot Equations

Same idea in other shifts

Asked 7× in all

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
6 Apr 2024, Shift 1 · Q29Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$ , $\vec{b}=3\hat{i}+4\hat{j}-5\hat{k}$ and a vector $\vec{c}$ be such that…HardNumerical 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
13 Apr 2023, Shift 1 · Q9Let $\vec{a}=\hat{i}+4\hat{j}+2\hat{k}$ , $\vec{b}=3\hat{i}-2\hat{j}+7\hat{k}$ and $\vec{c}=2\hat{i}-\hat{j}+4\hat{k}$ . If a vector…MediumSingle correct
25 Jun 2022, Shift 2 · Q26Let $\vec{b} = \hat{i} + \hat{j} + \lambda\hat{k}$ , $\lambda \in \mathbb{R}$ . If $\vec{a}$ is a vector such that…HardNumerical value
4 Aug 2021, Shift 2 · Q85Let $\vec a=-\hat i+\hat j$ and $\vec b=\hat i+\hat j-\hat k$ be two given vectors. If a vector $\vec c$ satisfies…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.