JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let

\vec{a}

be a vector which is perpendicular to the vector

3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}

. If

\vec{a}\times\left(2\hat{i}+\hat{k}\right)=2\hat{i}-13\hat{j}-4\hat{k}

, then the projection of the vector

\vec{a}

on the vector

2\hat{i}+2\hat{j}+\hat{k}

is :

(1) $\frac{1}{3}$
(2)1
(3) $\frac{5}{3}$ Official answer
(4) $\frac{7}{3}$

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.