Vector Question

Could someone give me a hand with the following vector quesion please?

I need to simplify: $(x-y).(x-y)+(x+y).z-(x+z).y$ where $x,y,z$ are vectors.
But I am a bit confused as what to do. Help appreciated.

For the dot product, $(a+b).(c+d) = a.c + b.c + a.d + b.d$ i.e. you can just multiply out the brackets.

Cheers, I had done that originally but when i came back to it it just didn't seem right.
You wouldn't mind still though perhaps doing a couple of steps of it for me, once its multiplied out I am not quite sure what to do...

Could someone give me a hand with the following vector quesion please?

I need to simplify: $(x-y).(x-y)+(x+y).z-(x+z).y$ where $x,y,z$ are vectors.
But I am a bit confused as what to do. Help appreciated.

For vectors, it's easier if you see it as column vectors. So your equation would translate to
(1,-1,0).(1,-1,0) + (1,1,0).(0,0,1) - (1,0,1).(0,1,0)

Note that for dot products, the answer would always be in scalar form, meaning it'll end up as a numerical answer.

(1,-1,0).(1,-1,0) = 1x1 + (-1)x(-1) + 0x0 = 1 + 1 + 0 = 2
Similarly,
(1,1,0).(0,0,1) = 0
(1,0,1).(0,1,0) = 0

So
$(x-y).(x-y)+(x+y).z-(x+z).y$
= (1,-1,0).(1,-1,0) + (1,1,0).(0,0,1) - (1,0,1).(0,1,0)
= 2 + 0 + 0
= 2

Initially I assumed $-yx$ = $-(-xy) = xy$ but now I am not so sure...

As I said earlier, x.y = y.x. The dot product is commutative. And yes, these are all just scalars (but that shouldn't make any difference to how you approach them).

Right, see I wasn't sure if $(x-y).(x-y)$
was $(x \times x) -(x \times y )- (y \times x )+ (y \times y)[br]$
i.e. the cross product of each vector.
I have only ever used dot products on column vectors before now.

You can treat x and y as if they are column vectors, for all it matters.

i just can't get my head round that for some reason... Sorry to be a pain but you couldn't perhaps tell me if the multiplication i done above is then correct?

Yeah, the multiplication you did was fine, that's why I didn't correct it.