JEE Main 2022MathematicsVector AlgebraEasyMCQ

JEE Main 2022 — Vector Algebra Question with Solution

JEE Main 2022 (28 Jul Shift 2)

Question

Let S be the set of all a∈R for which the angle between the vectors u→=alogebi^-6j^+3k^ and v→=logebi^+2j^+2alogebk^,b>1 is acute. Then S is equal to

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Show full solutionCorrect option: B
Correct answer
BΦ

Step-by-step explanation

Given,

 u→=alogebi^-6j^+3k^ and v→=logebi^+2j^+2alogebk^ 

For angle to be acute u→·v→>0

⇒alogebi^-6j^+3k^.logebi^+2j^+2alogebk^>0

⇒alogeb2-12+6alogeb>0 ∀b>1

Let y=alogeb2-12+6alogeb

Now let logeb=t⇒t>0 as b>1

Now y=at2+6at-12>0,∀ t>0

Since y>0, so a>0 & D<0

⇒D=36a2+48a<0

⇒a∈-43,0 but a>0,

So, a∈ϕ

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About this question

This is a previous-year question from JEE Main 2022, covering the Vector Algebra chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.