Two vectors P → and Q → have equal magnitudes. If the magnitude of P → + Q → is n…

Two vectors P→ and Q→ have equal magnitudes. If the magnitude of P→+Q→ is n times the magnitude of P→-Q→, then angle between P→ and Q→ is

  1. sin-1n-1n+1

  2. cos-1n-1n+1
  3. sin-1n2-1n2+1
  4. cos-1n2-1n2+1

Solution

|P→|=|Q→|=x  …i

|P→+Q→|=n|P→-Q→|

P2+Q2+2PQcosθ=n2P2+Q2-2PQcosθ

Using (i) in above equation,

cosθ=n2-11+n2

θ=cos-1n2-1n2+1

Asked in: JEE Main 2021 (20 Jul Shift 2)

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