JEE Main 2019MathematicsVector AlgebraMediumMCQ

JEE Main 2019 — Vector Algebra Question with Solution

JEE Main 2019 (12 Jan Shift 2)

Question

Let a→, b→ and c→ be three unit vectors, out of which vectors b→ and c→ are non-parallel. If α and β are the angles which vector a→ makes with vectors b→ and c→ respectively and a→×b→×c→=12b→, then α-β is equal to :

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Show full solutionCorrect option: D
Correct answer
D30o

Step-by-step explanation

a→×b→×c→=b→2⇒a→.c→b→-a→.b→c→=b→2

Since, b→ is not parallel to c→⇒a→.c→=12⇒accosβ=12⇒cosβ=12 and

a→.b→=0⇒abcosα=0⇒cosα=0

⇒β=π3 and α=π2

∴α-β=π2-π3=π6

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About this question

This is a previous-year question from JEE Main 2019, 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.