Section 13.2: Derivatives and Integrals of Vector Functions

If \(\mathbf{r}(t) = \mathbf{a}\cos \omega t + \mathbf{b}\sin \omega t\), where \(\mathbf{a}\) and \(\mathbf{b}\) are constant vectors, show that \(\mathbf{r}(t) \times \mathbf{r}'(t) = \omega \mathbf{a} \times \mathbf{b}\).