Find the equation of the plane passing through the following points: `(1,\ 1,\ 1),\ (1,\ -1,\ 2)a n d\ (-2,\ -2,\ 2)dot`

Explanation

We have to find the equation of plane passing though point (1, 1, 1), (1,-1,2) and (-2, -2,2)

Then the equation of the plane pasing through (1, 1, 1), (1,-1,2) and (-2, -2,2) is

`|(x-1,y-1,z-1),(1-1,-1-1,2-1),(-2-1,-2-1,2-1)|=0`

`|(x-1,y-1,z-1),(0,-2,1),(-3,-3,1)|=0`

`implies (x-1)(-2+3)-3(y-1)-6(z-1)=0`

` implies x-1-3y+3-6z+6=0`

`implies x-3y-6z+8=0`

`implies x-3y-6z=-8`