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If G(g), H(h) and P(p) are centroid' ort...

If `G(g), H(h)` and `P(p)` are centroid' orthocentre and circumcentre of a triangle and `x p+y h+z g=0`, then (x, y, z) is equal to

A

1, 1, -2

B

2, 1, -3

C

1, 3, -4

D

2, 3, -5

Text Solution

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The correct Answer is:
B
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`
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