The mysterious 4th dimension

Imagine we have a 2D plane-what would be the axis of the next,third dimension?Let's draw a line perpendicular to that plane.It's obvious that this line would be also perpendicular to every possible line in that plane,and also It's parallel to the third axis.
Now-wouldn't the axis of the 4th dimension have to be perpendicular to every possible line in 3D space?Is my reasoning correct,/sci/?

Of course you realise the third dimension we perceive is an illusionary one. We're really in fundamentally two dimensional space of which there are many parallel surfaces sitting next to each other.

Yes, you've guessed it - we're characters in a comic book.