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JEE Main 2022 — Mathematics in Physics Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Which of the following relations is true for two unit vector A^ and B^ making an angle θ to each other?

Choose an option

Show full solutionCorrect option: B
Correct answer
BA^-B^=A^+B^tanθ2

Step-by-step explanation

We know,

 1- cos θ=2sin2θ21+ cos θ=2cos2θ2

Now,a→+b→·a→+b→=a→2+2a→·b→+b→2⇒a→+b→·a→+b→=12+2×1×1×cosθ+12 ⇒a→+b→·a→+b→=21+cosθ⇒a→+b→2=4cos2θ2⇒a→+b→=2cosθ2  ...(1)

Similarly,

a→-b→·a→-b→=a→2-2a→·b→+b→2⇒a→-b→·a→-b→=12-2×1×1×cosθ+12⇒a→-b→·a→-b→=21-cosθ⇒a→-b→2=4sin2θ2⇒a→-b→=2sin θ2  ...(2)

Therefore,

A^-B^=A^+B^tanθ2

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About this question

This is a previous-year question from JEE Main 2022, covering the Mathematics in Physics chapter of Physics. 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.