Here is what I have done: I create three arrows by using the line command and then the stroke panel to add an arrowhead. I then make two duplicates of the arrow by pressing Alt + Shift + Left Arrow. Then, I use Effect -> 3D -> Rotate to rotate my 2D arrows into a right handed triad. The arrowheads lie in certain planes. When I go to unite the objects using the Pathfinder panel, it says: "The filter produced no results. Please select two overlapping paths."
I just want one object, essentially three right edges of a cube with arrowheads at the end, that I can use the 3D rotate command on to have an all-around orthogonal triad of vectors in my drawings.