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(D) The points of trisection divide the line segment $AB$ in the ratio $1:2$ and $2:1$ internally.Let the points be $P$ and $Q$ such that $P$ divides

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$10$

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(D) The points of trisection divide the line segment $AB$ in the ratio $1:2$ and $2:1$ internally.Let the points be $P$ and $Q$ such that $P$ divides $AB$ in ratio $1:2$ and $Q$ divides $AB$ in ratio $2:1$.The $z$-coordinate of a point dividing the segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in ratio $m:n$ is given by $\frac{mz_2 + nz_1}{m+n}$.For $z_1$ (ratio $1:2$):$z_1 = \frac{1(6) + 2(4)}{1 + 2} = \frac{6 + 8}{3} = \frac{14}{3}$.For $z_2$ (ratio $2:1$):$z_2 = \frac{2(6) + 1(4)}{2 + 1} = \frac{12 + 4}{3} = \frac{16}{3}$.Therefore,$z_1 + z_2 = \frac{14}{3} + \frac{16}{3} = \frac{30}{3} = 10$.

If $z_1$ and $z_2$ are the $z$-coordinates of the points of trisection of the line segment joining the points $A(2, 1, 4)$ and $B(-1, 3, 6)$,then $z_1 + z_2 =$

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