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For three non-zero vectors a → ,   b → and c → , if a →     b →     c → = 4 , then a → × b → + 2 c →   b → × c → - 3 a →   c → × 3 a → + b → is equal to

Options

  1. A12
  2. B16
  3. C84
  4. D144

Correct answer

D. 144

Step-by-step solution

a → × b → + 2 c → b → × c → - 3 a → c → × 3 a → + b → = a → × b → + 2 a → × c → b → × c → - 3 b → × a → 3 c → × a → + c → × b → = a → × b → b → × c → 3 c → × a → + 2 a → × c → - 3 b → × a → c → × b → = 3 a → × b → b → × c c → × a → + 6 a → × b → b → × c → c → × a → = 9 a → b → c → 2 = 9 × 16 = 144

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