I am doing vector analysis. I have figured out that the following expression won't be simplified in *Mathematica*:

```
Simplify[Dot[x, y] - Dot[y, x]]

```

I think the reason is that x and y could be matrices, so generally the operation does not commute. But for a vector, the commutation relation should hold. What I don't know is how to tell *Mathematica* to consider x and y to be vectors.

Also, how can I expand `Cross[x + y, z]` to be `Cross[x, y] + Cross[y, z]`? I tried to use `Expand` and `ExpandAll` but neither worked.

BTW, in *Mathematica*, is it possible to define a abstract row/column vector without explicitly specifying the number of entries?