Question:

Three mutually perpendicular lines have direction ratios $(1,1,0)$, $(1,0,1)$, $(0,1,1)$ and pass through $(1,0,1)$, $(1,1,0)$, $(0,1,1)$ respectively. The volume of the tetrahedron formed by them and the plane $x+y+z=1$ is $V$. Find $16V^2$.