Plane

Interpolate plane \(ax+by+cz+d=0\) through points

Variant 1
\((2{,}4,4)\), \((3{,}4,3)\) and \((3{,}1,6)\)
Hint
Follow the same scenario as for line interpolation.
Resolution
We first deduce the parametric form \(\alpha: (2{,}4,4)+t(1{,}0,-1)+s(1,-3{,}2)\).

We then eliminate parameters (in this particular case we may add all equations together).
Result
The equation of the plane is: \(x+y+z-10=0\).
Variant 2
\((6{,}4,6)\), \((3{,}5,4)\) and \((5{,}2,3)\)
Result
\(x+y-z-4=0\)
Variant 3
\((5{,}4,7)\), \((4{,}5,5)\) and \((2{,}2,6)\)
Result
\(-x+y+z-6=0\)
Variant 4
\((6{,}3,5)\), \((3{,}2,7)\) and \((5{,}1,4)\)
Result
\(x-y+z-8=0\)