Two vectors A → and B → have equal magnitudes. If magnitude of A → + B → is equal to…

Two vectors A→ and B→ have equal magnitudes. If magnitude of A→+B→ is equal to two times the magnitude of A→-B→, then the angle between A→ and B→ will be 
  1. cos-135
  2. cos-113
  3. sin-113
  4. sin-135

Solution

Given: A→+B→=2A→-B→ 

We have, 

A2+A2+2A2cosθ=4A2+A2-2A2cosθ

Simplifying we get 

2A2+2A2cosθ=8A2-8A2cosθ

⇒1+cosθ=4-4cosθ

  ⇒5cosθ=3⇒cosθ=35⇒θ=cos-135

Asked in: JEE Main 2022 (29 Jun Shift 1)

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