## Thomas' Calculus 13th Edition

$7x-5y-4z=6$
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, $7x-5y-4z=6$