Let $v_1,$dots,$v_k$ be the points in $R^3$ and suppose that for

$j=1,$dots,$k$ an object with mass $m_j$ is located at point $v_j.$

Physicists call such objects point masses. The total mass of

the system of point masses is $m=m_1+$cdots$+m_k.$ The center of

gravity $($or center of mass$)$ of the system is

$\frac{?}{\text{b}\text{a}\text{r}}(v)=\frac{1}{m}[m_1{v}_1+$cdots$+m_k{v}_k].$

Point

$v_1,=(6,-4,1),4g$

$v_2,=(5,4,-2),10g$

$v_3,=(-6,-1,-3),4g$

$v_4,=(-7,7,4),2g$

Compute the center of gravity of the system consisting of the point masses above.

The center of gravity is at $\frac{?}{\text{b}\text{a}\text{r}}(v)=1,,$

$($Simplify your answers.$)$