JEE Main 2020MathematicsVector AlgebraMediumNumerical

JEE Main 2020 — Vector Algebra Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

Let the position vectors of points 'A' and 'B' be i^+j^+k^ and 2i^+j^+3k^, respectively. A point 'P' divides the line segment AB internally in the ratio λ:1λ>0. If O is the origin and OB→·OP→-3OA→×OP→2=6 then λ is equal to

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Show full solutionCorrect answer: 0.8
Correct answer
0.8

Step-by-step explanation

Position vector of P is OP→=a→+λb→λ+1 ∵  OB→·OP→-3|OA→×OP→|2=6

⇒  b→·a→+λb→λ+1-3a→×a→+λb→λ+12=6

 ⇒a→·b→+λ|b→|2λ+1-3λ2(λ+1)2|a→×b→|2=6

⇒  6+λ.14λ+1-3λ2(λ+1)2·6=6

⇒  18λ2(λ+1)2+6=6+8λλ+1

⇒  18λλ+12-8λλ+1=0 λλ+1≠0

⇒  10λ=8⇒  λ=0.8

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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.