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 =

Question

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 =, ( 1 , 1 , - 2 ), ( 2 , 1 , - 3 ), ( 1 , 3 , - 4 ), ( 2 , 3 , - 5 )

MARKS App · Accepted Answer

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

Search any question & find its solution

Looking for more such questions to practice?