It depends on what you mean by `BA`
There is a dot product, and in 3 dimensions, there is a cross product.
Let's say `A=<a,b,c>` and `B=<x,y,z>`
Then `A*B=ax+by+cz` so you end up with a number
But `AxxB=<bz-cy,cx-az,ay-bx>`, so you end up with another vector
If you mean dot product, then:
If you mean cross product, then the formulas are a lot more complicated, and in fact, what you have is probably as simple as the expression can get.
You could use the following:
`AxxB+CxxD=(A-C)xx(B-D)+AxxD+CxxB` and `AxxB=-BxxA` and `BxxB=0` to get:
but that isn't any more simple than what you started with.