Consider, on a plane, the triangle $ ABC, $ vectors $ \vec x,\vec y,\vec z, $ real variable $ \lambda >0 $ and $ M,N,P $ such that $$ \left\{\begin{matrix} \overrightarrow{AM}=\lambda\cdot\vec x\\\overrightarrow{AN}=\lambda\cdot\vec y \\\overrightarrow{AP}=\lambda\cdot\vec z \end{matrix}\right. . $$Find the locus of the center of mass of $ MNP. $ Dan Brânzei and Gheorghe Iurea