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JEE Main201910 Apr 2019Morning ShiftMathematicsVector AlgebraActual

Let A 3 , 0 , - 1 , B 2 , 10 , 6 and C 1 , 2 , 1 be the vertices of a triangle and M be the mid-point of A C . If G divides B M in the ratio, 2 : 1 , then c o s ∠ G O A ( O being the origin) is equal to

Options

  1. A1 30
  2. B1 6 10
  3. C1 15
  4. D1 2 15

Correct answer

C. 1 15

Step-by-step solution

∵     M is mid point of A C   &   G divides B M in the ratio 2 : 1 internally ∴   G is centroid of △ A B C ∴   G = 3 + 1 + 2 3 , 0 + 2 + 10 3 , - 1 + 1 + 6 3 = 2 , 4 , 2 ∴     O A → = 3 i → + 0 j → - k →   &   O G → = 2 i → + 4 j → + 2 k → ∴     cos ∠ G O A = O A → . O G → O A → O G → = 6 - 2 10 24 = 4 10   2 6 = 1 15

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