Originally Posted by

**Plato** No it makes absolutely no sense to anyone.

You simply do not understand points, much less vectors.

If $\displaystyle (a,b,c)$ is a point and $\displaystyle (x,y,z)$ is a point then of course you are free to name the two any thing you wish.

But given $\displaystyle P: (a,b,c)~\&~Q: (x,y,z)$ are two points then they come named. Therefore, you may not rename them. The example you gave does not occur. Once two points are labeled, now we can address vectors.

Now it is true that often we say $\displaystyle \vec{a}$ is a vector.

We don't have two point specified. But the ideas of *length and direction* are still there.

Consider two pairs of points $\displaystyle P: (2,-3,5)~\&~Q: (5,-6,1)$ and the pair $\displaystyle A: (-1,3,2)~\&~B: (2,0,-2)$.

There are **four different points**.

BUT $\displaystyle \overrightarrow {PQ} = \overrightarrow {AB} $, **one vector**.

A vector is an equivalence class of objects that have the same length and direction.