If `G(barg), H(barh)` and `P(barp)` are centroid, orthocenter and circumcenter of a triangle and `xbarp + ybarh + zbarg =0` then `(x, y, z)=`

Options

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

Answer

B

Explanation

We know that, orthocentre, entroid and circumentre of a triangle are collinear and centroid divides orthocentre and cicumcentre in the ratio `2:1`

By using internally division,
`(2p+1h)/(2+1)=g implies2p+h-3g=0`
But it is given, ` xp+yh+zg=0`
`thereforex=2, y=1 and z=-3`