Školjka

%V0 Let $M$ be an interior point of the tetrahedron $ABCD$. Prove that $$\stackrel{\longrightarrow }{MA} \text{vol}(MBCD) + \stackrel{\longrightarrow }{MB} \text{vol}(MACD) + \stackrel{\longrightarrow }{MC} \text{vol}(MABD) + \stackrel{\longrightarrow }{MD} \text{vol}(MABC) = 0\text{.}$$ ($\text{vol}(PQRS)$ denotes the volume of the tetrahedron $PQRS$).