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If a → ,   b → and c → are three non-zero and non-coplanar vectors such that a → b → c → = 4 , then the value of a → + 3 b → - c → ⋅ a → - b → × a → - 2 b → - 3 c → is equal to

Options

  1. A40
  2. B44
  3. C48
  4. D52

Correct answer

D. 52

Step-by-step solution

a → + 3 b → - c → ⋅ a → - b → × a → - 2 b → - 3 c → = 1 3 - 1 1 - 1 0 1 - 2 - 3 a → b → c → = 1 3 - 3 - 3 - 1 - 2 + 1 × 4 = 13 × 4 = 5 2

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