Mathematics

Mathematics

Problem

If the position vectors of fixed points

A

and

B

are

\vec{a}

and

\vec{b}

, and the position vector

\vec{c}

of vertex

C

satisfies

|\vec{c}| = 3

, find the value of

|\vec{g} - \frac{\vec{a} + \vec{b}}{3}|

, where

\vec{g}

is the position vector of the centroid.

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