Right, but I think I made a mistake in post #5. Unless you are telling me that my post #5 is correct and now I am wrong (which is very possible).Maybe geogebra didn't actually indicate that the 'zero vector' <0, 0, 0> itself is undefined (because it is). Instead, I'd expect the message meant we can't plot a zero vector as an arrow.
The zero vector is a special case; it's defined as a vector having no direction. Any vector whose components are all zero has no magnitude. Without any length, an arrow can't point toward anything.
The scalar number zero is known as "the additive identity" because the sum of adding 0 to a Real number is the same Real number. That's a useful identity, in algebra. A zero vector is like "the vector-additive identity" because adding a zero vector to another vector doesn't change anything. That's useful in vector arithmetic.
That's not what you wrote in post #5. Each of the six vectors in post #5 have a defined magnitude and direction. None of them are zero vectors.