Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

$AB=\sqrt{2},AC=\sqrt{3},BC=\sqrt{5}$, so the angle at A is a right angle and the base area is $\frac{\sqrt{6}}{2}$. Volume = base area × height gives height $h=\sqrt{6}$. The edge $A{A}_1$ is perpendicular to the base, along $\overrightarrow{AB}\times \overrightarrow{AC}=(1,2,1)$, so $A_1=(1,0,1)\pm (1,2,1)$, i.e. (2,2,2) or (0,-2,0).