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MHT CET2016MathematicsVector Algebra

If G ( g → ) , H ( h → ) and P ( p → ) are centroid, orthocenter and circumcenter of a triangle and x p → + y h → + z g → = 0 then x , y , z =

Options

  1. A( 1 , 1 , - 2 )
  2. B( 2 , 1 , - 3 )
  3. C( 1 , 3 , - 4 )
  4. D( 2 , 3 , - 5 )

Correct answer

B. ( 2 , 1 , - 3 )

Step-by-step solution

We know that, in a triangle centroid (G), orthocenter (H) and circumcenter (P) are always collinear and G divides the line segment PH in ratio 1:2 So using section formula, g ¯ = 2 p ¯ + h ¯ 3 ⇒ 3 g ¯ = 2 p ¯ + h ¯ ⇒ 2 p ¯ + h ¯ − 3 g ¯ = 0

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