MHTCET 2016 Math Solved Paper

(b) Since, orthocentre, centroid and circumcentre of a triangle are collinear whereas centroid divides orthocentre and circumcentre in the ratio of 2:1. By internally division formula

2p+1h

2+1

= g
⇒ 2p + h - 3g = 0
As, xp + yh + zg = 0
Hence, x = 2,y = 1 and z = -3