JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

Let

\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

\vec r\cdot(\alpha\hat i+2\hat j+\hat k)=3

and

\vec r\cdot(2\hat i+5\hat j-\alpha\hat k)=-1

\alpha\in\mathbf R

, then the value of

\alpha+|\vec r|^2

is equal to :

(1)9
(2)11
(3)13
(4)15Official answer

Official answer

Option 4

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

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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
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

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.