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If a → + 2 b → + 3 c → × b → + 2 c → + 3 a → ⋅ c → + 2 a → + 3 b → = 54 , where a → ,   b → and c → are 3 non-coplanar vectors, then the value of a → ⋅ a → a → ⋅ b → a → ⋅ c → b → ⋅ a → b → ⋅ b → b → ⋅ c → c → ⋅

Options

  1. A9
  2. B3
  3. C6
  4. D12

Correct answer

A. 9

Step-by-step solution

a → + 2 b → + 3 c → b → + 2 c → + 3 a → c → + 2 a → + 3 b → = 5 4 1 2 3 3 1 2 2 3 1 a → b → c → = 5 4 1 - 5 - 2 - 1 + 3 7 a → b → c → = 5 4 a → b → c → = 3 Also a → ⋅ a → a → ⋅ b → a → ⋅ c → b → ⋅ a → b → ⋅ b → b → ⋅ c → c → ⋅ a → c → ⋅ b → c → ⋅ c → = a → b → c → 2 = 9

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