JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q30

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

Let

\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

(\vec{a}+\vec{b})\times\vec{c}=2(\vec{a}\times\vec{b})+24\hat{j}-6\hat{k}

and

(\vec{a}-\vec{b}+\hat{i})\cdot\vec{c}=-3

. Then

|\vec{c}|^2

is equal to _____.

Official answer

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Solving Vector Equations with Cross Products

Same idea in other shifts

Asked 8× in all

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
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
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
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
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
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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.