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Let Δ O A B be an equilateral triangle with side length unity ( O being the origin). Also, M and N are the points of trisection of A B , M being closer to A and N being closer to B . Position vectors of A , B , M and N are a → , b → , m → and n → respectively, then the value of m → ⋅ n → is equal to

Options

  1. A1 2
  2. B2 3
  3. C13 18
  4. D4 9

Correct answer

C. 13 18

Step-by-step solution

m → = 2 a → + b → 3 , n → = a → + 2 b → 3 m → ⋅ n → = 1 9 2 a → + b → ⋅ a → + 2 b → = 1 9 2 a → 2 + 2 b → 2 + 5 a → ⋅ b → = 1 9 2 + 2 + 5 × 1 × 1 × 1 2 = 13 18

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