JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B. NTA dropped this question from the final key; it is left out of every count on this site.

Let

\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}

\vec{b} = \hat{i} + \hat{j} + \hat{k}

and

\vec{c}

be a vector such that

\vec{a} + \left(\vec{b} \times \vec{c}\right) = \vec{0}

and

\vec{b} \cdot \vec{c} = 5

. Then, the value of

3\left(\vec{c} \cdot \vec{a}\right)

is equal to ___.

Official answer

Dropped by NTA (marks given to all)

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
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.