Question 5
(CZS 3) Let $M$ be an interior point of the tetrahedron $ABCD$. Prove that
$$\overrightarrow{MA}\operatorname{vol}(MBCD)+\overrightarrow{MB}\operatorname{vol}(MACD)+\overrightarrow{MC}\operatorname{vol}(MABD)+\overrightarrow{MD}\operatorname{vol}(MABC)=0$$
($\operatorname{vol}(PQRS)$ denotes the volume of the tetrahedron $PQRS$).
$$\overrightarrow{MA}\operatorname{vol}(MBCD)+\overrightarrow{MB}\operatorname{vol}(MACD)+\overrightarrow{MC}\operatorname{vol}(MABD)+\overrightarrow{MD}\operatorname{vol}(MABC)=0$$
($\operatorname{vol}(PQRS)$ denotes the volume of the tetrahedron $PQRS$).