## Thomas' Calculus 13th Edition

${\bf u}\times{\bf v}$ has length $0$ and no direction ${\bf v}\times{\bf u}$ has length $0$ and no direction
See Property 5 of the cross product (page 714) ${\bf w}={\bf u}\times{\bf 0}={\bf 0}$ (zero vector has length 0 and no direction) ${\bf v}\times{\bf u}=-{\bf w}=(-{\bf 0})={\bf 0}$ ${\bf u}\times{\bf v}$ has length $0$ and no direction ${\bf v}\times{\bf u}$ has length $0$ and no direction