Answer
$x+y-2z=7$
Work Step by Step
Since, we have $t=1+s$ and $3-3t=4+s$
After solving, we get $s=-1$ and $t=1+s=1-1=0$
The normal to the plane is $n=\lt -2,-2,4 \gt$
We know that the standard equation of a plane passing through the point $(x_0,y_0,z_0)$ is written as: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
Then for point $(0,3,-2)$, we have
$-2(x-0)-2(y -3)+4(z+2)=0$
or, $-2x-2y+4z=-14$
or, $x+y-2z=7$
