Twist one end of each together, with the 3 sticking out at 90 degrees from each other.
Kink an "arrow" onto the end of the one you're calling $\uv z$.
Kink a ball onto the end of the one you're calling $\uv x$.
Write down your color key indicating $\hat x, \hat y, \hat z$ in order for these to form a right-handed coordinated system, that is, $\hat x \times \hat y = \hat z$. Confirm your key with your instructor before going on.
Use GeoGebra to confirm your *point of view*
Try this in GeoGebra: Create a point called "PNP" (get it??)
Now, rotate the coordinate system around with your mouse until the point PNP appears to be directly on top of the origin. Now you are looking at the origin from a point which has a coordinate like $(+k,-k,+k)$ (where $k$ is some positive constant).
