## Thomas' Calculus 13th Edition

Build a counterexample. Let ${\bf u}$ =${\bf i, v}$ =${\bf 2i,w}$ =${\bf 3i}.,$ The cross products ${\bf u}\times{\bf v}$ and ${\bf u}\times{\bf w}$ both equal ${\bf 0}$, because the cross product of parallel vectors is the zero vector. So, we have ${\bf u}\times{\bf v}={\bf u}\times{\bf w}, \quad {\bf u}\neq {\bf 0}$, but ${\bf v}\neq {\bf w}$