Answer
See the explanation
Work Step by Step
Four points define a planar patch only if they all lie in the same plane.
That means there exists a plane equation of the form:
$ax+by+cz+d=0$
that all four points satisfy.
Three points always define a plane.
Let’s find the plane through A,B,C.
These have coordinates:
A(0,0,0)
B(1,0,0)
C(0,1,0)
The plane containing them is clearly the XY-plane, i.e.
z=0
Check if the fourth point lies in that plane
D(0,0,1) → has z=1
Substitute into the plane equation z=0:
$1\not=0$
so D does not lie in that plane.
Therefore, the given points cannot form the vertices of a planar patch.
