JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

\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

\vec{d}

satisfies

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

and

\vec{d}\cdot\vec{a}=24

, then

|\vec{d}|^2

is equal to

(1) $323$
(2) $313$
(3) $423$
(4) $413$ Official answer

Official answer

Option 4

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
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
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
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.