JEE Main 2023MathematicsVector AlgebraMediumMCQ

JEE Main 2023 — Vector Algebra Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

Let a→=i^+4j^+2k^,b→=3i^-2j^+7k^ and c→=2i^-j^+4k^. If a vector d→ satisfies d→×b→=c→×b→ and d→·a→=24, then d→2 is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D413

Step-by-step explanation

We have been given that

d→×b→=c→×b→

⇒(d→-c→)×b→=0

⇒d→-c→=λb→  (∵d→≠c→)

⇒d→=c→+λb→

It is given that a→·d→=24 

⇒a→·c→+λb→·a→=24

⇒6+λ(3-8+14)=24

⇒9λ=18

⇒λ=2

∴d→=c→+2b→

⇒d→=8i^-5j^+18k^

|d→|2=64+25+324=413

Hence, this is the correct option.

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About this question

This is a previous-year question from JEE Main 2023, 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.