JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q18

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

The set of all

\alpha

, for which the vectors

\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k}

and

\vec{b}=t\hat{i}-2\hat{j}-2\alpha t\hat{k}

are inclined at an obtuse angle for all

t\in\mathbb{R}

, is

(1) $[0,1)$
(2) $(-2,0]$
(3) $\left(-\frac{4}{3},0\right]$ Official answer
(4) $\left(-\frac{4}{3},1\right)$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Acute and Obtuse Angle Conditions

Same topic in other shifts

All Dot Product questions

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2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram $PQRS$ are given by $\vec{PQ} = \hat{j} + \hat{k}$ and $\vec{PS} = \hat{i} - \hat{j}$ . If the side…MediumSingle correct
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
7 Apr 2025, Shift 2 · Q15Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that…MediumSingle correct
8 Apr 2025, Shift 2 · Q14Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Let $\hat{c}$ be a unit vector in the plane of…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.