JEE Main 2021MathematicsVector AlgebraEasyNumerical

JEE Main 2021 — Vector Algebra Question with Solution

JEE Main 2021 (25 Feb Shift 1)

Question

Let a→=i^+2j^-k^, b→=i^-j^ and c→=i^-j^-k^ be three given vectors. If r→ is a vector such that r→×a→=c→×a→ and r→·b→=0, then r→·a→ is equal to

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Show full solutionCorrect answer: 12
Correct answer
12

Step-by-step explanation

r→-c→×a→=0

⇒ r→=c→+λa→

taking dot product with b→

Now, 0=b→·c→+λa→·b→

⇒ λ=-b→·c→a→·b→=-2-1=2

So, r→·a→=a→·c→+2a→2=0+2×6=12

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About this question

This is a previous-year question from JEE Main 2021, 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.