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

Explanation

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

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

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

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

`implies 4x-3(y+1)+2z=0`

` implies 4x-3y+2z-3=0`

Now put fourth point (3,3,0) in this

`implies 4(3)-3(3)+2(0)-3=0`

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