JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 29 June 2022, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let

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

\vec{b} = 3\hat{i} - \beta\hat{j} + 4\hat{k}

and

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

where

\alpha, \beta \in \mathbf{R}

, be three vectors. If the projection of

\vec{a}

\vec{c}

\frac{10}{3}

and

\vec{b} \times \vec{c} = -6\hat{i} + 10\hat{j} + 7\hat{k}

, then the value of

\alpha + \beta

is equal to :

(1)3Official answer
(2)4
(3)5
(4)6

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Scalar and Vector Projection

Same idea in other shifts

Asked 11× in all

2 Apr 2025, Shift 1 · Q11If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$ , $\hat{i}+2\hat{j}-2\hat{k}$ and…MediumSingle correct
8 Apr 2024, Shift 2 · Q18Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ , $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$ and…MediumSingle correct
1 Feb 2024, Shift 2 · Q17Consider a $\Delta ABC$ where $A(1,3,2)$ , $B(-2,8,0)$ and $C(3,6,7)$ . If the angle bisector of $\angle BAC$ meets the line $BC$ at $D$ ,…MediumSingle correct
25 Jul 2022, Shift 2 · Q17Let $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a}\times\vec{b}=2\hat{i}-\hat{k}$ and…MediumSingle correct
30 Jul 2022, Shift 2 · Q88Let $OABC$ be a parallelogram, $O$ be the origin, $A\,(2, 4, -5)$ and $C\,(b, 2, 3)$ . If $P\,(a, a, a)$ and $Q\,(9-a^2, 3, a-1)$ ,…HardNumerical value
26 Jun 2022, Shift 2 · Q16Let $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$ , $\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$ be…MediumSingle correct
26 Aug 2021, Shift 2 · Q87If the projection of the vector $\hat{i}+2\hat{j}+\hat{k}$ on the sum of the two vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and…EasyNumerical value
17 Mar 2021, Shift 2 · Q89Let $\overrightarrow{x}$ be a vector in the plane containing vectors $\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}$ and…HardNumerical value

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.