JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}

and

\vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}

. If

\left(\left(\vec{a} \times \vec{b}\right) \times \hat{i}\right) \cdot \hat{k} = \dfrac{23}{2}

, then

\left|\vec{b} \times 2\hat{j}\right|

is equal to

(1)4
(2)5Official answer
(3) $\sqrt{21}$
(4) $\sqrt{17}$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 4× in all

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
26 Jun 2022, Shift 1 · Q16If $\vec{a} \cdot \vec{b} = 1$ , $\vec{b} \cdot \vec{c} = 2$ and $\vec{c} \cdot \vec{a} = 3$ , then the value of…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.