vector identity

Three vectors $\vec{p}$, $\vec{q}$, and $\vec{r}$ are given as $\vec{p} = \hat{i} + \hat{j} + \hat{k}$ $\vec{q} = \hat{i} + 2\hat{j} + 3\hat{k}$ $\vec{r} = 2\hat{i} + 3\hat{j} + 4\...