Question

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

Answer 1

Correct Answer - B
We know that, orthocentre, centroid and circumcentre of a triangle are collinear and centroid divides orthocentre and circumcentre in the ratio 2 : 1
By using internally division
`(2p+1h)/(2+1)=g`
`Rightarrow 2p+h-3g=0`
But it is given xp+yh+zg=0
`therefore x=2, y=1 and z=-3`