JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 17 March 2021, Shift 1, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

Let

\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}

and

\vec{b}=7\hat{i}+\hat{j}-6\hat{k}

. If

\vec{r}\times\vec{a}=\vec{r}\times\vec{b}

\vec{r}\cdot(\hat{i}+2\hat{j}+\hat{k})=-3

, then

\vec{r}\cdot(2\hat{i}-3\hat{j}+\hat{k})

is equal to :

(1)8
(2)10
(3)12Official answer
(4)13

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 20× in all

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5 Apr 2024, Shift 1 · Q29Let $\vec a=\hat i-3\hat j+7\hat k$ , $\vec b=2\hat i-\hat j+\hat k$ and $\vec c$ be a vector such that…MediumNumerical value
5 Apr 2024, Shift 2 · Q18Let $\vec{a} = 2\hat{i}+5\hat{j}-\hat{k}$ , $\vec{b} = 2\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{c}$ be three vectors such that…MediumSingle correct
8 Apr 2024, Shift 2 · Q17Let $\vec{a} = 4\hat{i} - \hat{j} + \hat{k}$ , $\vec{b} = 11\hat{i} - \hat{j} + \hat{k}$ and $\vec{c}$ be a vector such that…HardSingle correct
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
27 Jan 2024, Shift 1 · Q19Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$ , $\vec{b}=3(\hat{i}-\hat{j}+\hat{k})$ . Let $\vec{c}$ be the vector such that…MediumSingle 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.