Question

Is it true to say that any vectors on a plane will be parallel to the plane ?

Answer 1

You should probably get a second opinion about this.
But, I would think that if we had something like the xy-plane, with your class x-axis and y-axis, a vector can only be parallel to one plane at a time.

It can be fully horizontal, parallel to the x-plane, perpendicular to the y-plane.
It can be fully vertical, parallel to the y-plane, perpendicular to the x-plane.

Answer 2

yes i think so.

Answer 3

yes