# I dont know how write the vector signs but the question is simplify BA-BC

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### 1 Answer

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:

`B*A-B*C=B*(A-C)`

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:

`BxxA-BxxC=BxxA+CxxB`

`=(B-C)xx(A-B)+BxxB+CxxA`

`=(B-C)xx(A-B)+CxxA`

but that isn't any more simple than what you started with.