Answer
$7x-5y-4z=6$
Work Step by Step
The plane passing through the points $(1,1,-1),(2,0,2), (0,-2,1)$
Now, $\overrightarrow{a}=\lt 1,-1,3 \gt; \overrightarrow{b}=\lt -1,-3,2 \gt$
and $\overrightarrow{a}\times \overrightarrow{b}=\lt -1,-3,2 \gt= 7i-5j-4k$
Suppose the equation of plane is $7x-5y-4z=D$
For point $(1,1,-1)$:
$ 7(1)-5(1)-4(-1)=d \implies d=6 $
Hence, $7x-5y-4z=6$
