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Let a → = x 2 i ^ - 3 j ^ + x + 3 k ^ and b → = i ^ + 3 j ^ - x - 3 k ^ be two vectors such that a → = b → . If angle between 4 a → + 7 b → and 7 a → - 4 b → is equal to θ , then cos ⁡ 2 θ is equal to

Options

  1. A- 1 2
  2. B3 2
  3. C- 1
  4. D1 5

Correct answer

C. - 1

Step-by-step solution

∵ a → · b → = x 2 - 9 - x 2 - 9 = 0 ⇒ a → ⊥ b → 4 a → + 7 b → ⋅ 7 a → − 4 b → = 28 a → 2 − 28 b → 2 + 33 a → ⋅ b → = 0   as  a → = b → ⇒ θ = 90 o ⇒ cos ⁡ 2 θ = - 1

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