Could you please explain what is wrong with the expression: ?
I know that and are correct. But why the above one isn't?
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.