[tex]\overrightarrow{AB} = 4\vec{i} +3\vec{j}\\ \overrightarrow{BC} = \vec{i}-\vec{j}\\ \\ \overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}\quad (\text{proprietate}) \\ \\ \begin{array}{rcl} \Rightarrow \overrightarrow{AC} &=&\overrightarrow{AB} + \overrightarrow{BC} \\ &=& (4\vec{i} +3\vec{j}) + ( \vec{i}-\vec{j}) \\ &=& (4\vec{i}+\vec{i})+(3\vec{j}-\vec{j}) \\ &=& 5\vec{i}+2\vec{j} \end{array} \\ \\ \\ \overrightarrow{AC} = (m+1)\vec{i} + (m-2)\vec{j} \\ \\
[/tex]
[tex]\Rightarrow m+1 = 5,\quad m-2 = 2 \Rightarrow \boxed{m = 4}[/tex]
