Problems

Prove that the point $X$ lies on the line $AB$ if and only if $\overrightarrow{OX}=t\overrightarrow{OA}+(1-t)\overrightarrow{OB}$ for some $t$ and any point $O$.

Several points are given and for some pairs $(A,B)$ of these points the vectors $\overrightarrow{AB}$ are taken, and at each point the same number of vectors begin and end. Prove that the sum of all the chosen vectors is $\overrightarrow{0}$.