B Is Center of Mass a vector or scalar quantity?

[Cutter Ketch]

@Cutter Ketch I agree with your statements. In fact I was going to write something similar in my previous post. I get that they have a difference; that the direction for position doesn't even mean anything without a coordinate system, while for the other quantities it does. But is that a good enough reason to say that position is not a vector? I wasn't sure.
Seeing @robphy's post I understand the difference ( it's so subtle).

Well, since we make vectors to represent position and add those vectors to find center of mass and many other manipulations, I have been careful not to say that position isn't a vector. I can certainly understand the point of view that things we represent with vectors are vector quantities. However if you ask me if it is a vector quantity that sounds like a different question to me. I hear does that physical property have a direction and a magnitude? In any case I'm pretty sure failing to make the distinction was the reason for the OPs confusion and incredulous responses before I chimed in, so I wanted to draw the line between math and physics.

 

[robphy]

Another way to distinguish the 3-component-objects that describe "position" from those that describe "displacement"
is to say that
a "displacement" (from one position to another) is a 3-d vector (whose magnitude is independent of choice of origin and orientation of axes).
but a "position" is merely a labeling by 3 numbers (whose values (and sum-of-squares) depend on the choice of origin and choice of orientation of axes).
Again, it wouldn't mean anything (independent of frame) to generally add two positions... but one can get a weighted average of positions.
Thus, everyone will agree on where the center of mass is located (its position in space)... but not necessarily agree on how to label it.

Similarly, an "elapsed time" (from one clock reading to another) is a 1-d vector (in some abstract space) whose magnitude is independent of choice of origin (of time).
However, a "clock reading" is merely a labeling by one number (whose value depends on the choice of origin of time).
Generally, it wouldn't mean anything (independent of origin) to generally add two clock readings ... but one can get an average of clock readings.
Everyone will agree on when the halfway-time occurs... but not necessarily agree on how to label it.