In every german high school book about vector geometry, points in 2d or 3d cartesian coordinate systems are denoted like $P(2|-1|5)$. Very rarely one also reads something like $P = P(2|-1|5)$. But I have never seen $P = (2|-1|5)$ (or $|$ replaced by $,$ or $;$).
What is the origin of this notation and what is the reason for using it?
And the other way around: The notation above seems to be so "hard coded" into the german abitur problems that letting students write $P = (2|-1|5)$ feels to be wrong in some way though I don't see any reason for it. Are there any pretty-minded reasons why this notation should not be used?
However the first notation seems to be ugly because if you write something like:
$$ A(1|2|3), B(4|5|6) \implies \vec{AB} = \begin{pmatrix}3\\3 \\3 \end{pmatrix} $$
Doesn't seem to make sense because $A(1|2|3), B(4|5|6)$ doesn't read like a statement.
However
$$ A = (1|2|3), B = (4|5|6) \implies \vec{AB} = \begin{pmatrix}3\\3 \\3 \end{pmatrix} $$
seems to be much more like math notation is used in allmost all other areas.
Similar problem with something like:
$$ B(4|5|6) \text{ and } \vec{AB} = \begin{pmatrix}3\\3 \\3 \end{pmatrix}\implies A(1|2|3) $$
Would be great if someone could clarify the points above.