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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}

on

\vec{c}

is

\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 2× 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

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.