JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 June 2022, Shift 1, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

\vec{a} \cdot \vec{b} = 1

\vec{b} \cdot \vec{c} = 2

and

\vec{c} \cdot \vec{a} = 3

, then the value of

\left[\vec{a} \times (\vec{b} \times \vec{c}),\ \vec{b} \times (\vec{c} \times \vec{a}),\ \vec{c} \times (\vec{b} \times \vec{a})\right]

is :

(1)0Official answer
(2) $-6\,\vec{a} \cdot (\vec{b} \times \vec{c})$
(3) $12\,\vec{c} \cdot (\vec{a} \times \vec{b})$
(4) $-12\,\vec{b} \cdot (\vec{c} \times \vec{a})$

Official answer

Option 1

NTA final key.

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: VTP BAC-CAB Expansion

Same idea in other shifts

Asked 4× in all

27 Jul 2022, Shift 1 · Q13Let $\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ . If…MediumSingle correct
29 Jul 2022, Shift 1 · Q10Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$ . Let $\vec{c}$ be a vector satisfying…MediumSingle correct
31 Aug 2021, Shift 2 · Q75Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $\vec{r}$ …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 108 of the 174 JEE Main shifts held from 2017 to 2026.