Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors such that $\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a} \cdot \mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}$, then the unit vector in the direction of $\mathbf{r}$ is