Show that the following points are coplanar: `(0,\ 4,\ 3),\ (-1,\ -5,\ -3),\ (-2,\ -2,\ 1)a n d\ (1,\ 1,\ -1)dot`

Explanation

We have to prove that the point (0, 4, 3), (-1, -5,-3), (-2, -2, 1) and (1, 1,-1) are coplanar

Then the equation of the plane pasing through (0, 4, 3), (-1, -5,-3),and (-2, -2, 1) is

`|(x-0,y-4,z-3),(-1-0,-5-4,-3-3),(-2-0,-2-4,1-3)|=0`

`|(x,y-4,z-3),(-1,-9,-6),(-2,-6,-2)|=0`

`implies -18x+10(y-4)-12(z-3)=0`

` implies 9x-5(y-4)+6(z-3)=0`

` implies 9x-5y+6z+2=0`

Now put fourth point (1,1,-1) in this

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