For a $3 \times 3$ matrix $A$, the singular value decomposition is $A = USV^T$. For $U = [u_1 u_2 u_3]$, I'm attempting to understand why the dot product of the cross product of $u1$ and $u_2$, $u_3$ is always $1$. In otherwords, dot(cross(u1,u2), u3) = 1.
I understand that $1$ comes from the cosine in the definition of the dot product, but I'm unable to have an intuitive understanding beyond that.