Let a → ,   b → and c → be three unit vectors, out of which vectors b → and c…

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 :
  1. 90o
  2. 60o
  3. 45o
  4. 30o

Solution

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

Asked in: JEE Main 2019 (12 Jan Shift 2)

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