Geometry Tip: Instead of solving the linear system, you can directly find the normal vector of the required plane by taking the cross product of the normal vectors of the two given perpendicular planes: $\vec{n} = \vec{n}_1 \times \vec{n}_2 = \langle1, 2, -2\rangle \times \langle3, 2, 1\rangle = \langle6, -7, -4\rangle$.