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 idea in other shifts

Asked 3× in all

27 Jan 2024, Shift 1 · Q28The least positive integral value of $\alpha$ , for which the angle between the vectors $\alpha\hat{i}-2\hat{j}+2\hat{k}$ and…EasyNumerical value
28 Jul 2022, Shift 2 · Q77Let S be the set of all $a\in\mathbb{R}$ for which the angle between the vectors $\vec{u}=a(\log_e b)\hat{i}-6\hat{j}+3\hat{k}$ 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 108 of the 174 JEE Main shifts held from 2017 to 2026.