Planes that are parallel to axis.

Question

If a plane is parallel to the $x$ axis then it's perpendicular to the $YZ$ plane. That's what my book is saying but I have a question. If a plane is parallel to the $X$ axis then shouldn't it be also in parallel to the $Y$ axis thus it's also perpendicular to $XZ$ axis ?? Can someone explain it to me ?

Answer 1

There are many planes parallel to the $x$-axis, but the common property of all of them is that their normal vector lies in the $yz$-plane. Now consider that planes are defined to be orthogonal iff their normal vectors are, and you get the result.