Ta có: `\vec(AI) = \vec(AB)+ u\vec(BC)`
`\vec(AG) = \vec(AB) + \vec(BG) = \vec(AB) + 2/3. 1/2(\vec(BM)+ \vec(BN))`
`= \vec(AB) + 1/3\vec(BM) + 1/3\vec(BC) + 1/3\vec(CN)`
`=\vec(AB) -1/3. 2/3\vec(AB) + 1/3\vec(BC) -1.3 1/2\vec(AB)`
`=\vec(AB) -2/9\vec(AB) + 1/3\vec(BC) -1/6\vec(AB)`
`=11/18\vec(AB) + 1/3\vec(BC)`
Vì `A, G, I` thẳng hàng
`-> \vec(AI)` và `\vec(AG) ` cùng phương
`-> ` $\dfrac{1}{\dfrac{11}{18}} = \dfrac{u}{\dfrac{1}{3}}$
`Leftrightarrow 1/3 = (11u)/(18)`
`Leftrightarrow u = (18)/(33) = (6)/(11)`