JEE Main 2020MathematicsVector AlgebraHardNumerical

JEE Main 2020 — Vector Algebra Question with Solution

JEE Main 2020 (09 Jan Shift 1)

Question

If the vectors, p→=a+1i^+aj^+ak^,q→=ai^+a+1j^+ak^ and r→=ai^+aj^+a+1k^a∈R are coplanar and 3p→.q→2-λr→×q→2=0 , then the value of λ is ________

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Show full solutionCorrect answer: 1
Correct answer
1

Step-by-step explanation

a+1aaaa+1aaaa+1=0⇒a+1+a+a=0⇒a=-13
P→=23i^-13j^-k^
Q→=13-i^+2j^-k^
R→=13-i^-j^+2k^
P→.Q→=19-2-2+1=-13
R→×Q→=19ijk-12-1-1-12=19i4-1-j-2-1+k1+2=193i+3j+3k=i+j+k3
R→×Q→=133⇒R→×Q→2=13 3P→.Q→2-λR→×Q→2=0
3.19-λ.13=0⇒λ=1

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About this question

This is a previous-year question from JEE Main 2020, 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.