Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Let the equation of the plane be $a(x+2)+b(y+2)+c(z-2)=0$.

Since the plane passes through the points $(1,1,1)$ and $(1,-1,2)$, we can determine the ratios of $a$, $b$, and $c$.

Substituting the points into the plane equation yields $\frac{a}{1}=\frac{b}{-3}=\frac{c}{-6}$.

Thus, the equation of the plane is:

$$\frac{x}{-8}+\frac{y}{8/3}+\frac{z}{8/6}=1$$

The required sum is $12$.