Solution
= Solution
Use $(0,1,1)$ as an anchor. Two directions in the required <plane> are
$$
\mathbf u=(2,0,2),\qquad \mathbf v=(4,1,0).
$$
Their <cross product> is $(-2,8,2)$, so a <normal vector> is $\mathbf n=(-1,4,1)$. The <Cartesian equation of a plane> is
$$
\mathbf n\cdot[(x,y,z)-(0,1,1)]=0,
\qquad \boxed{-x+4y+z=5.}
$$
Direct substitution verifies all three given points. The independent direction <vectors> ensure the <plane> is uniquely determined.