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Let a → ,   b → ,   c → be three vectors of magnitude 3 ,   4 ,   5 respectively, satisfying a → b → c → = 60 . If a → + 2 b → + 3 c → · a → × c → × b → + b → = λ , then λ is equal to

Options

  1. A16
  2. B32
  3. C20
  4. D40

Correct answer

B. 32

Step-by-step solution

Given, a → b → c → = 3 · 4 · 5 = 60 Also, a → b → c → = 60 ⇒ a → b → c → = a → b → c → ⇒ a → , b → , c → are mutually perpendicular vectors Also, a → × c → × b → + b → = a → · b → c → - c → · b → a → + b → = b → Hence, a → + 2 b → + 3 c → · b → = 2 b → 2 = 32

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