Can a plane be perpendicular in two other planes if those planes are not parallel to each other?

Question

I have to write equation of a plane which passes through a point and its perpendicular to 2 planes , but before I start solving I was thinking if can a plane be perpendicular to two other planes , if those 2 others are not parallel to each other ( linearly dependent) ?

Answer 1

Yes: take two perpendicular planes, and a third plane perpendicular to their intersection.

For instance: with an orthonormal basis in $\mathbf R^3$, the $(x\text{-}y)$, $(y\text{-}z)$ and $(x\text{-}z)$ planes.