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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 28 July 2022, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

Let S be the set of all a∈Ra\in\mathbb{R} for which the angle between the vectors u⃗=a(log⁡eb)i^−6j^+3k^\vec{u}=a(\log_e b)\hat{i}-6\hat{j}+3\hat{k} and v⃗=(log⁡eb)i^+2j^+2a(log⁡eb)k^, (b>1)\vec{v}=(\log_e b)\hat{i}+2\hat{j}+2a(\log_e b)\hat{k},\ (b>1) is acute. Then S is equal to :
  1. (1)(−∞,−43]\left(-\infty,-\frac{4}{3}\right]
  2. (2)Φ\PhiOfficial answer
  3. (3)(−43,0]\left(-\frac{4}{3},0\right]
  4. (4)(127,∞)\left(\frac{12}{7},\infty\right)

Official answer

Option 2

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
  1. 8 Apr 2024, Shift 1 · Q18The set of all α\alpha, for which the vectors a⃗=αti^+6j^−3k^\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k} and…MediumSingle correct
  2. 27 Jan 2024, Shift 1 · Q28The least positive integral value of α\alpha, for which the angle between the vectors αi^−2j^+2k^\alpha\hat{i}-2\hat{j}+2\hat{k} and…EasyNumerical 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.