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Smriti Ghosh
Asked: 2022-11-06T20:37:08+05:30 In:

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

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
A. 1
B. `1/2`
C. `1/3`
D. `2/3`
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  1. Correct Answer – C
    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`

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