Basically, the question is "Let $u, v$ and $w$ be vectors in $\mathbb{R^3}$. Determine whether the expression is defined." I'm lost - I thought I understood dot product until right now! The problems I've done that are similar always involve coordinates and it seems to make more sense.
an example of the problem i'm trying to work on: $(u•v)(v•w)$ how do you define this?
The dot product of two vectors in ℝ3 is a real number. So you have the product of two real numbers. Yes, that's well-defined.