If `veca, vecb` and `vecc` are position vectors of A,B, and C respectively of `DeltaABC` and `if|veca-vecb|=4,|vecb-vec(c)|=2, |vecc-veca|=3`, then the distance between the centroid and incenter of `triangleABC` is

Options

A. 1
B. `1/2`
C. `1/3`
D. `2/3`

Answer

C

Explanation

Let G be centroid and I be incenter.
`|vec(GI)|=|vec(OI)-vec(OG)|=|(2veca+3vecb+4vecc)/(9)-(veca+vecb+vecc)/(3)|`
`=|(-veca+vecc)/(9)|=3/9=1/3`