Answer
$x-2y-z=-3$
Work Step by Step
The line of intersection is given as: $a=u \times v$
where $u=\lt1,2,3\gt$ and $v=\lt2,-1,1\gt$
Thus, $a=u \times v=\lt5,5,-5\gt$ and $b=\lt3,-1,5\gt$
Now, $n=a\times b=\lt20,-40,-20\gt$
The general form of the equation of the plane is:
$a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
or, $ax+by+cz=ax_0+by_0+cz_0$
Plugging in the values $\lt20,-40,-20\gt$, we get
$20(x-3)-40(y-1)-20(z-4)=0$
After simplification, we get
$x-2y-z=-3$
