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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

Options

  1. Asin - 1 n - 1 n + 1
  2. Bcos - 1 n - 1 n + 1
  3. Csin - 1 n 2 - 1 n 2 + 1
  4. Dcos - 1 n 2 - 1 n 2 + 1

Correct answer

D. cos - 1 n 2 - 1 n 2 + 1

Step-by-step solution

| P → | = | Q → | = x     … i | P → + Q → | = n | P → - Q → | P 2 + Q 2 + 2 P Q cos θ = n 2 P 2 + Q 2 - 2 P Q cos θ Using   ( i ) in above equation, cos θ = n 2 - 1 1 + n 2 θ = cos - 1 n 2 - 1 n 2 + 1

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