Answer
$-20x+12y+z=7$
Work Step by Step
Since, we have $2t+1=s+2$ and $3t+2=2s+4$
After solving, we get $t=0$ and $s=-1+2t=-1$
The normal to the plane is $n=\lt -20,12,1 \gt$
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 $(1,2,3)$, we have
$-20(x-1)+12(y -2)+1(z-3)=0$
or, $-20x+20+12y-24+z-3=0$
or, $-20x+12y+z=7$
