In this particular example there is an even faster way to see that
must be outside of the triangle
, because
is even outside the cuboid spanned by the three corners of
. Indeed, for all points
in
it must be true that
![{\displaystyle {\begin{aligned}\min(0,1,-1)&\leq x\leq \max(0,1,-1)\\\min(1,1,2)&\leq y\leq \max(1,1,2)\\\min(2,5,2)&\leq z\leq \max(2,5,2)\end{aligned}}}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/896228ea049c1c1c58296002851d419d2cb325b4)
However, since the
and
coordinates of
do not satisfy the inequalities above,
is outside the cuboid, and hence outside of
.