5. [tex]\displaystyle\frac{BM}{BC}=\frac13\Rightarrow BM=\frac13BC[/tex]
[tex]\displaystyle\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}=\overrightarrow{AB}+\frac13\overrightarrow{BC}=\overrightarrow{AB}+\frac13(\overrightarrow{BA}+\overrightarrow{AC})=\overrightarrow{AB}+\frac13(-\overrightarrow{AB}+\overrightarrow{AC})=\frac23\overrightarrow{AB}+\frac13\overrightarrow{AC}[/tex]
6.
[tex]\displaystyle\alpha\in\left(\frac\pi2, \pi\right)\Rightarrow \cos x<0\\\sin^2x+\cos^x=1\Rightarrow \cos^2x=1-\sin^2x=\displaystyle\frac{16}{25}\Rightarrow|\cos x|=\frac{16}{25}\Rightarrow \cos x=-\frac45\\\\tg x=\displaystyle\frac{\sin x}{\cos x}=\frac{\frac35}{-\frac45}=-\frac34[/tex]
