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/?

>>6
Think of a vector in three space.  Time along one axis, and x and y along the other two.  We'll just ignore the third spacial direction so this example is visuable.  Now have the vector's tail at the origin and move the tip around in space keeping the magnitude fixed.  This is how an objects velocity vector acts.  It has a fixed magnitude equal to c.  Most of the time the largest component of that vector is in the time direction.  However, in order to increase the velocity in the x or y direction, we need to rotate the vector, thus minimizing the time component.  As you can see if you're not moving at all through space, then the time component is equal to c.  If you're moving through space with a velocity equal to c, then the time component must be zero.