Solution
= Solution
The three displacements from $Q_1$ are
$$
\mathbf u=(1,1,1)^T,\quad\mathbf v=(-1,2,1)^T,\quad\mathbf w=(0,3,2)^T.
$$
Here $\mathbf u\times\mathbf v=(-1,-2,3)^T$ and its <dot product> with $\mathbf w$ is zero. Because the <cross product> itself is nonzero, the first three points determine a <plane> and the fourth lies on it. Explicitly all four satisfy
$$
\boxed{-x-2y+3z=3}.
$$
Thus \b[the four points are coplanar].