# Thread: Cross product and vectors

1. ## Cross product and vectors

"Given that v and w are vectors such that v x w = 2i - j + 3k, find:
(v + 3w) x (2w - v)"

My working:
-> 2(v x w) -3(w x v)

Having a look at the solution, the equation needs to be further simplified: as 5(v x w) and what I do not understand is how you would be able to get to that equation. I understand the working out from after having simplified the equation - it is just this step of the answer that I am having difficulty with.

2. Note that

$\displaystyle \mathbf{w}\times\mathbf{v}=-\mathbf{v}\times\mathbf{w}.$

That is, I think, the missing piece.