JEE Main 2022MathematicsVector AlgebraMediumMCQ

JEE Main 2022 — Vector Algebra Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

Let a→ be a vector which is perpendicular to the vector 3i^+12j^+2k^. If a→×2i^+k^=2i^-13j^-4k^, then the projection of the vector a→ on the vector 2i^+2j^+k^ is

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Show full solutionCorrect option: C
Correct answer
C53

Step-by-step explanation

Given, a→×2i^+k^=2i^-13j^-4k^

Now multiplying both side by 3i^+12j^+2k^ we get,

⇒a→×2i^+k^×3i^+12j^+2k^

=2i^-13j^-4k^×3i^+12j^+2k^

⇒3i^+12j^+2k^.a→2i^+k^-6+2a→=i^j^k^2-13-43122

⇒0-6+2a→=i^j^k^2-13-43122

a→=3i^+2j^-5k^

Now, projection of a→ on vector 2i^+2j^+k^ is a→·2i^+2j^+k^3=53

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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.