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If a → , b → and c → are three vectors, such that a → = 2 , b → = 3 , c → = 4 , a → ⋅ c → = 0 , a → ⋅ b → = 0 and the angle between b → and c → is π 3 , then the value of a → × 2 b → - 3 c → is equal to

Options

  1. A12 3
  2. B6 3
  3. C3 3
  4. D5

Correct answer

A. 12 3

Step-by-step solution

2 b → - 3 c → 2 = 4 b → 2 + 9 c → 2 - 12 b → ⋅ c → = 36 + 144 - 12 × 3 × 4 × 1 2 = 10 8 2 b → - 3 c → = 6 3 As we know that, a → × 2 b → - 3 c → 2 + a → ⋅ 2 b → - 3 c → 2 = a → 2 2 b → - 3 c → 2 ⇒ a → × 2 b → - 3 c → 2 + 0 = 4 × 10 8 ⇒ a → × 2 b → - 3 c → = 12 3

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