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Let a → and b → are unit vectors such that a → + b → = 3 2 , then the value of 2 a → + 7 b → ⋅ 4 a → + 3 b → + 2020 a → × b → is equal to

Options

  1. A133 4
  2. B133
  3. C30
  4. D120

Correct answer

A. 133 4

Step-by-step solution

a → + b → 2 = 9 4 ⇒ 1 + 1 + 2 a → ⋅ b → = 9 4 ⇒ a → ⋅ b → = 1 8 2 a → + 7 b → ⋅ 4 a → + 3 b → + 2020 a → × b → = 8 a → 2 + 6 a → ⋅ b → + 0 + 28 a → ⋅ b → + 21 b → 2 + 0 = 8 + 6 × 1 8 + 28 × 1 8 + 21 = 29 + 17 4 = 133 4

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