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Let O A B C be a regular tetrahedron with side length unity, then its volume (in cubic units) is

Options

  1. A3 2
  2. B6 2
  3. C1 3 2
  4. D1 6 2

Correct answer

D. 1 6 2

Step-by-step solution

Let the position vector of O , A , B , C are 0 → , a → , b → , c → respectively O A → = a → , O B → = b → , O C → = c → O A → = O B → = O C → = 1 [Given] Volume = 1 6 O A → O B → O C → = 1 6 a → b → c → … … i ∴ a → b → c → 2 = a → ⋅ a → a → ⋅ b → a → ⋅ c → b → ⋅ a → b → ⋅ b → b &

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