Let $\hat{a}, \hat{b}$ be unit vectors. If $\vec{c}$ be a vector such that the angle between $\hat{a}$ and $\vec{c}$ is $\frac{\pi}{12}$, and $\hat{b}=\vec{c}+2(\vec{c}\times\hat{a})$, then $\left|6\vec{c}\right|^2$ is equal to :

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q16

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

Let

\hat{a}, \hat{b}

be unit vectors. If

\vec{c}

be a vector such that the angle between

\hat{a}

and

\vec{c}

\frac{\pi}{12}

, and

\hat{b}=\vec{c}+2(\vec{c}\times\hat{a})

, then

\left|6\vec{c}\right|^2

is equal to :

(1) $6(3-\sqrt{3})$
(2) $3+\sqrt{3}$
(3) $6(3+\sqrt{3})$ Official answer
(4) $6(\sqrt{3}+1)$

Official answer

Option 3

NTA final key (2022 Session 1).

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

Same idea in other shifts

Asked 8× in all

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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
31 Jan 2024, Shift 2 · Q30Let $\vec{a}=3\hat{i}+2\hat{j}+\hat{k}$ , $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}$ be a vector such that…HardNumerical value
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.