JEE Main 2020MathematicsVector AlgebraEasyNumerical

JEE Main 2020 — Vector Algebra Question with Solution

JEE Main 2020 (06 Sep Shift 1)

Question

 If a→ and b→ are unit vectors, then the greatest value of 3|a→+b→|+|a→-b→| is
 

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

Let angle between a→ and b→=α.
So, 3|a→+b→|+|a→-b→|=32+2cosα+2-2cosα
=32×2cos2α2+2×2sin2α2
=23cosα2+sinα2

As α∈0,π⇒α2∈0,π2

So, given expression is

=23cosα2+sinα2
Thus, maximum value is=232+12=2×2=4

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About this question

This is a previous-year question from JEE Main 2020, 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.