JEE Main 2021MathematicsVector AlgebraEasyMCQ

JEE Main 2021 — Vector Algebra Question with Solution

JEE Main 2021 (25 Jul Shift 1)

Question

Let the vectors 2+a+bi^+a+2b+cj^-b+ck^, 1+bi^+2bj^-bk^ and 2+bi^+2bj^+1-bk^, ∀a,b,c∈R be co-planar. Then which of the following is true?

Choose an option

Show full solutionCorrect option: A
Correct answer
A2b=a+c

Step-by-step explanation

If the vectors are co-planar,

a+b+2a+2b+c-b-cb+12b-bb+22b1-b=0

Now R1↔R1-R2, R3↔R3-R2 

So a+1a+c-cb+12b-b101=0

⇒(a+1)2b-(a+c)(2b+1)-c(-2b)=0

⇒2ab+2b-2ab-a-2bc-c+2bc=0

⇒2b-a-c=0⇒2b=a+c

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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.