5. Find the equation of the plane determined by the three points

(0,1,1), (1,0,1), (1,1,0).

v = <1,0,1> - <0,1,1> = <1, -1, 0>

w = <1,1,0> - <0,1,1> = <1,0,-1>

The the normal to the plane, r, is given by

Consequently, the equation of the plane is

<1, 1, 1> · <x, y-1, z-1> = 0.

That is, x + y + z = 2.