If veca, vecb and vecc are position vect...

If `veca, vecb` and `vecc` are position vectors of A,B, and C respectively of `DeltaABC` and `if|veca-vecb|,|vecb-vec(c)|=2, |vecc-veca|=3`, then the distance between the centroid and incenter of `triangleABC` is

A

1

B

`(1)/(2)`

C

`(1)/(3)`

D

`(2)/(3)`

Verified by Experts

The correct Answer is:

C

Let G be centroid and I be incenter.
`|GI|=|OI-OG|=|(2a+3b+4c)/(9)-(a+b+c)/(3)|`
`=|(-a+c)/(9)|=(3)/(9)=(1)/(3)`

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