For the following two (02) items: Let A(1, -1, 0) , B(-2, 1, 8) and...

Let the coordinates of the fourth vertex $D$ be $(x, y, z)$.

In a parallelogram, the diagonals bisect each other. Therefore, the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.

Midpoint of $AC = \left( \dfrac{1 - 1}{2}, \dfrac{-1 + 2}{2}, \dfrac{0 + 7}{2} \right) =$\left(0, \dfrac{1}{2},\dfrac{7}{2} \right)

Midpointof BD = \left( \dfrac{-2 + x}{2},\dfrac{1 + y}{2}, \dfrac{8 + z}{2} \right)

Equating the $corresponding coordinates:<br><br>\dfrac{-2 + x}{2} =0 \Rightarrow x = 2$

$\dfrac{1 + y}{2} = \dfrac{1}{2} \Rightarrow y = 0$

$\dfrac{8 + z}{2} = \dfrac{7}{2}$ \Rightarrow z = -1$<br><br>The coordinates of the fourth vertex$D$are$(2, 0, -1)$.<br><br>Answer:$(2, 0, -1)