How to visualize isometric Projection?

I read the definition of Isometric Projection from this pdf that Projection plane intersects each coordinate axis in which the object is defined (principal axes) at the same distant from the origin.

But we know that projection plane is 2D plane where z-component is either zero or constant, so how is it possible projection plane intersects each coordinate axis?This sentence isn't understanding in that pdf ,what does it mean?

I also read that Projection vector makes equal angles with all of the three principal axes.Isometric projection is obtained by aligning the projection vector with the cube diagonal.

My question is how to visualize projection from 3D space to projection plane(2D) where diagonal(projection vector) makes equal angle with 3 principal axis of below image(which is projection plane image after projection):

In the hope a picture is worth a thousand words (cross your eyes to fuse the images into a stereogram):

The simplest way to arrange that the projection plane meets the Cartesian axes at equal distances from the origin is to make the intersection points the standard basis vectors $(1, 0, 0)$, $(0, 1, 0)$, and $(0, 0, 1)$. The equation containing these points is $x + y + z = 1$. It's reasonable to define $Z = x + y + z$, which is a linear coordinate whose level planes are parallel to the projection plane.