Solution
= Solution
Use displacements from $P_1$, since coplanarity of points concerns an affine <plane> that need not contain the origin. The three displacement <vectors> are
$$
\mathbf u=(0,1,1)^T,\quad\mathbf v=(1,2,1)^T,\quad\mathbf w=(2,3,2)^T.
$$
Their <cross product> is $\mathbf u\times\mathbf v=(-1,1,-1)^T$ and its <dot product> with $\mathbf w$ is $-1$. Since the <scalar triple product> is nonzero,
\b[The four points do not lie in a common plane.]