A plane $\pi_2$ intersects $\pi_1$: $4x-2y+7z-3=0$ at right angles. Two points lie on $\pi_2$: $A(3,2,0)$ and $B(2,-2,1)$. Write a cartesian equation for $\pi_2$.
I know that the normals of these two planes must be perpendicular since the planes are perpendicular. So if $n_2=(a,b,c)$ is the normal for plane $2$ and $n_1=(4,-2,7)$ is the normal for plane $1$ then the dot product between $n_1$ and $n_2$ is $0$.
Not sure where else to go with this question.