1. ## Cross product

Hi!

Could you please explain what is wrong with the expression: $u \times v \times w$ ?

I know that $u \times (v \times w)$ and $(u \times v) \times w$ are correct. But why the above one isn't?

Thanks!

2. Originally Posted by saeros
Hi!

Could you please explain what is wrong with the expression: $u \times v \times w$ ?

I know that $u \times (v \times w)$ and $(u \times v) \times w$ are correct. But why the above one isn't?

Thanks!
the cross product is a very specific kind of operation. it is a binary operation, which means it operates on two elements at a time. the kind of elements it operates on is 3-dimensional vectors. so you have to apply the cross product on two 3-d vectors at a time. so your first expression is essentially mathematically meaningless, while the other two would be acceptable.