How to correctly show units with a vector? Supposed I have an position vector $$\vec{r}=\begin{pmatrix}
10.0 & -30.0 & 25.0\end{pmatrix}$$ expressed in $\mathrm{millimeters}$.
What is the correct notation to display $\vec{r}$

*

*$\begin{pmatrix}
10.0 \\ -30.0 \\ 25.0\end{pmatrix}\text{ [mm]}$

*$\begin{pmatrix}
10.0\text{ [mm]} \\ -30.0\text{ [mm]} \\ 25.0\text{ [mm]}\end{pmatrix}$

*$(40.3113\text{ [mm]}) \begin{pmatrix}0.24807 \\ -0.7442 \\ 0.6202\end{pmatrix}$
If the answer is 2. then why add all those redundunt units when all elements of a vector have to be of the same unit. If you have a long list of values then usualy you present this a table with the units in the header (and not on each element). What if the units are complex (with powers and fraction), do we really have to write them out for each element?
How would you consicely write out a vector while describing the units those values are in also at the same time?
PS. I did not post this in the Math SE because they have never heard of units :-) and only physics deals with real situations.
 A: I would say 1. and 2. are correct. In the first you are multiplying by the scalar 1 mm.
Also elements of vectors dont need to have the same units.
Just consider the 4-vector (3 sec, 1 µm, 82 ly, 5.6 parsec)
A: Both 1 and 2 are perfectly fine notation.  As someone who teaches introductory physics a lot, I would use either in class and accept either as correct from a student.  #3 expresses the meaning perfectly clearly but is not the usual form of expression.  I would certainly have no problem if a student wrote that in my class, for instance.
A: I write it as 10i + 20j + 5k and set the scale somewhere before the calculations. Of course, you could add it after the vector, but that just doesn't look neat and tidy.
Or you could write the unit vector on the side and multiply the magnitude (with correct units) into it. That could also clarify things. I guess it just depends on how you grasp things and what's clearer to you. As long as you keep others in the loop then it should be okay.
A: The correct notation is that of multiplying the whole thing by a unit (as a multiplication constant):
(a,b,c)*mm
