Answer
$(\dfrac{11}{9},\dfrac{26}{9},\dfrac{-7}{9})$
Work Step by Step
Here, the equation of a normal plane is: $n=\lt 2,-1,2 \gt$
Now, $2x-y+2z=-2 \implies 2(3+2t)-(2-t)+2(1+2t)=-2$
Thus, $9t =-8$ or, $ t=\dfrac{-8}{9}$
The parametric equations are: $x=3+2(\dfrac{-8}{9})=\dfrac{11}{9}; y=2-(-\dfrac{2}{3})=\dfrac{26}{9}; z=1+2(\dfrac{-8}{9})=\dfrac{-7}{9}$
Therefore, the line will meet the plane at the point: $(\dfrac{11}{9},\dfrac{26}{9},\dfrac{-7}{9})$
