35. Four points not lying in the same plane are given by their coordinates: $A\left(x_{1}, y_{1}, z_{1}\right) ; B\left(x_{2}, y_{2}, z_{2}\right), C\left(x_{3}, y_{3}, z_{3}\right)$ and $D\left(x_{4}, y_{4}, z_{4}\right)$. Find the coordinates of a point $M$ such that the forces proportional to the vectors $\overrightarrow{M A}, \overrightarrow{M B}, \overrightarrow{M C}, \overrightarrow{M D}$ and applied at point $M$ balance each other, i.e., $\overrightarrow{M A} + \overrightarrow{M B} + \overrightarrow{M C} + \overrightarrow{M D} = \overrightarrow{0}$

$35 *$. In space, $n$ points are given: $A_{1}, A_{2}, \ldots, A_{n}$ with coordinates $\left(x_{1}, y_{1}, z_{1}\right),\left(x_{2}, y_{2}, z_{2}\right), \ldots,\left(x_{n}, y_{n}, z_{n}\right)$ and with masses $m_{1}, m_{2}, \ldots, m_{n}$ placed at these points. Write the formula for the coordinates of the center of mass of these points.
35. We already know that the radius vector $\vec{r}_{0}$ of the center of mass of $n$ points $A_{1}, A_{2}, \ldots, A_{n}$ with masses $m_{1}, m_{2}, \ldots, m_{n}$, determined by the radius vectors $\vec{r}_{1}=\overrightarrow{O A}_{1}, \vec{r}_{2}=\overrightarrow{O A}_{2}, \ldots, \vec{r}_{n}=\overrightarrow{O A}_{n}$, is expressed by the formula: $\vec{r}_{0}=\frac{m_{1} \overrightarrow{r_{1}}+m_{2} \overrightarrow{r_{2}}+\ldots+m_{n} \overrightarrow{r_{n}}}{m_{1}+m_{2}+\cdots+m_{n}}$ (see problem $6 \S 5$ ). If all radius vectors are expressed in coordinates, we get:

$$
x_{0}=\frac{\sum_{k=1}^{n} m_{k} x_{k}}{\sum_{k=1}^{n} m_{k}} ; \quad y_{0}=\frac{\sum_{k=1}^{n} m_{k} y_{k}}{\sum_{k=1}^{n} m_{k}} ; \quad z_{0}=\frac{\sum_{k=1}^{n} m_{k} z_{k}}{\sum_{k=1}^{n} m_{k}}
$$