JEE Main 2021MathematicsVector AlgebraMediumMCQ

JEE Main 2021 — Vector Algebra Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

Let a→ and b→ be two vectors such that |2a→+3b→|=|3a→+b→| and the angle between a→ and b→ is 60°. If 18a→ is a unit vector, then |b→| is equal to : 

Choose an option

Show full solutionCorrect option: D
Correct answer
D5

Step-by-step explanation

Given that 

18a→ is a unit vector.

|a→|=8
|2a→+3b→|2=|3a→+b→|2

We know thata→ · b→  = a→ b→ cos θ ,
⇒4|a→|2+9|b→|2+12|a→||b→|cos60°=9|a→|2+|b→|2+6|a→||b→|cos60°
⇒5|a→|2=8|b→|2+6|a→|||b→∣cos60°
⇒564=8|b→|2+68·|b→|12
⇒|b→|2+3|b→|-40=0⇒b→+8|b→|-5=0
⇒|b→|=5

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About this question

This is a previous-year question from JEE Main 2021, 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.