$\text{ Direction ratios of normal to plane through the points (-1, }1,1),(1,-1,1)\text{ and perpendicular to the plane }x+2y+2z=5\text{ are }$

Plane is passing through the points A(-1, 1, 1), B(1,-1, 1)

Let any point on the plane be $P(x,y,z)$

$\text{ Then vector }\overrightarrow{AP}\times \overrightarrow{AB}\text{ is perpendicular to the vector }\widehat{i}+2\widehat{j}+2\widehat{k}$

$\text{ which is normal to the plane }x+2y+2z=5\text{. }$

$\text{ Hence, equation of plane is }\left|\begin{array}{ccc}x-(-1)& y-1& z-1\\ 1-(-1)& -1-1& 1-1\\ 1& 2& 2\end{array}\right|=0\text{ or }$

$2x+2y-3z+3=0$