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If a → , b → , c → be three unit vectors perpendicular to each other, then 2 a → + 3 b → + 4 c → ⋅ a → × b → + 5 b → × c → + 6 c → × a → is equal to

Options

  1. A18
  2. B0
  3. C4
  4. D32

Correct answer

D. 32

Step-by-step solution

2 a → + 3 b → + 4 c → ⋅ a → × b → + 5 b → × c → + 6 c → × a → = 10 a → b → c → + 18 a → b → c → + 4 a → b → c → = 32 a →   b →   c → = 32   as  a →   b →   c → = 1

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