Show that the four point `(0,-1,-1),(4,5,1),(3,9,4)a n d(-4,4,4)` are coplanar and find the equation of the common plane.

Explanation

Equation of plane passing through
`(0, –1, –1)` is `a(x – 0) + b(y + 1) + c(z + 1) = 0 …(i) `


The above equation passes through
`(4, 5, 1)` and `(3, 9, 4) `

So,

` 4a + 6b + 2c = 0 or 2a + 3b + c = 0 …(ii) `

and `3a + 10b + 5c = 0 …(iii)`
From (ii) and (iii), we get

`a/(15-10)=-b/(10-7)=c/(20-9)`


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