How to interpretation (visualize) number of common trends in the Johansen cointegration test with three series?

[eviews1]

Assume that we run the Johansen cointegration test for three series that are I(1) (e.g. series: x, y and z). How can one interpret (visualize) number of common trends. Let’s assume the following scenarios of the test results.
a) The test shows 2 cointegrating vectors => 1 common trend.
Interpret(visualize): e.g. y follows x, z follows x (or z follows y) => one common trend is represented by x.

b) The test shows 1 cointegrating vector => 2 common trend.
Interpret(visualize): e.g. y follows x, z wanders by itself. So two common trends are represented by x and z.
How do we call these three series cointegrated if two of them (x and z) are wandering independent of each other?

Or should be the case with 1 cointegrating vector be valid to call three variables cointegrated if a single cointegrating equation look like this alpha1*x+alpha2*y+alpha3*z+gamma=0 where alpha1,2,3 are non-zero (in the b scenario above we may think that a cointegrating equation has z but with zero coefficient).