
\[ -5\vv{MA}+3\vv{MB}=\vv{0}\]

\[ -5\vv{MA}+3\left(\vv{MA}+\vv{AB}\right)=\vv{0}\]

\[ -5\vv{MA}+3\vv{MA}+3\vv{AB}=\vv{0}\]

\[ -2\vv{MA}+3\vv{AB}=\vv{0}\]

\[ 2\vv{AM}=-3\vv{AB}\]

\[ \vv{AM}=-\frac{3}{2}\vv{AB}\]

\begin{center}
\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (M) at (-7.5,0);
\fill (A) circle (2pt) node[below]{A};
\fill (B) circle (2pt) node[below]{B};
\fill (M) circle (2pt) node[below]{M};
\draw (M) -- (B);
\draw (2.5,0.1) -- (2.5,-.1);
\draw (-2.5,0.1) -- (-2.5,-.1);
\draw (-5,0.1) -- (-5,-.1);
\end{tikzpicture}
\end{center}
