Explanation

(c) Given, $m_{1} = 6\ kg,\ m_{2} = 4\ kg$
$\mathbf{v}_{\mathbf{1}} = 5\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + 10\widehat{\mathbf{k}}\ ,\ \ v_{2} = 10\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + 5\widehat{\mathbf{k}}$
The velocity of centre of mass is
$\mathbf{v} = \frac{m_{1}\mathbf{v}_{\mathbf{1}} + m_{2}\mathbf{v}_{\mathbf{2}}}{m_{1} + m_{2}}$
$= \frac{6\left( 5\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + 10\widehat{\mathbf{k}} \right) + 4\left( 10\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + 5\widehat{\mathbf{k}} \right)}{6 + 4}$
$= \frac{70\widehat{\mathbf{i}} - 20\widehat{\mathbf{j}} + 80\widehat{\mathbf{k}}}{10} = 7\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + 8\widehat{\mathbf{k}}$