Plane perpendicular to another

Find a plane β perpendicular to α (normal (2, 1, 2)) through P(14, 9, 6).

Step-by-step solution

Two planes are perpendicular if their normals are perpendicular.
Choose a normal perpendicular to that of α and through P.
Check that the dot product of the two normals is 0.
There are infinitely many planes perpendicular to α through P: all those containing the normal direction of α.

Result: β has normal (-3, 4, 1) and passes through P(14, 9, 6).

Do not confuse a perpendicular plane with a parallel one: perpendicular means perpendicular normals, not parallel normals.