JEE Main 2019MathematicsVector AlgebraEasyMCQ

JEE Main 2019 — Vector Algebra Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

Let a→=3i^+2j^+2k^ and b→=i^+2j^-2k^ be two vectors. If a vector perpendicular to both the vectors a→+b→ and a→-b→  has the magnitude 12 then one such vector is:

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Show full solutionCorrect option: B
Correct answer
B4(2i^-2j^-k^)

Step-by-step explanation

a→=3i^+2j^+2k^,b→=i+2j^-2k^
∵ α→=a→+b→=4i^+4j^
 β→=a→-b→=2i^+4k^
∴ α→×β→=i^j^k^440204=i^16-j^16+k^-8=16i^-16j^-8k^
∴ Unit vector perpendicular to  α→& β→ is
n^=α→×β→α→×β→=2i^-2j^-k^3
∴ Required vector =122i^-2j^-k^3=42i^-2j^-k^

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About this question

This is a previous-year question from JEE Main 2019, 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.