JEE Main 2022MathematicsVector AlgebraMediumMCQ

JEE Main 2022 — Vector Algebra Question with Solution

JEE Main 2022 (25 Jul Shift 2)

Question

Let a→=i^-j^+2k^ and let b→ be a vector such that a→×b→=2i^-k^ and a→·b→=3. Then the projection of b→ on the vector a→-b→ is:

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Show full solutionCorrect option: A
Correct answer
A221

Step-by-step explanation

Given,

a→=i^-j^+2k^ , a→×b→=2i^-k^ and a→·b→=3

Now using the formula a→×b→2+a→·b→2=a→2·b→2sin2θ+a→2·b→2cos2θ

⇒a→×b→2+a→·b→2=a→2·b→2sin2θ+cos2θ=a→2·b→2

We get,

⇒2i^-k^2+32=i^-j^+2k^2b→2

⇒b→2=5+96=146=73

Now finding a→-b→=a→2+b→2-2a→b→=6+73-6=73

Now projection of b→ on a→-b→=b→·a→-b→a→-b→

=b→·a→-b→2a→-b→=3-7373

=221

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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.