JEE Main 2022MathematicsVector AlgebraEasyNumerical

JEE Main 2022 — Vector Algebra Question with Solution

JEE Main 2022 (25 Jun Shift 2)

Question

Let b→=i^+j^+λk^,λ∈ℝ. If a→ is a vector such that a→×b→=13i^-j^-4k^ and a→·b→+21=0, then b→-a→·k^-j^+b→+a→·i^-k^ is equal to

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Show full solutionCorrect answer: 14
Correct answer
14

Step-by-step explanation

Let a→=xi^+yj^+zk^

So,i^j^k^xyz11λ=i^λy-z+j^z-λx+k^x-y

On comparing with 13i^-j^-4k^ we get,

⇒λy-z=13,z-λx=-1,x-y=-4

and x+y+λz=-21

⇒ Clearly, λ=3,x=-2,y=2 and z=-7

So, b→-a→=3i^-j^+10k^ and b→+a→=-i^+3j^-4k^

⇒b→-a→·k^-j^+b→+a→·i^-k^=11+3

=14

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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.