The unit vector $\mathbf{u}$ is given by $\mathbf{a}$ divided by the magnitude of $\mathbf{a}$, which is $\sqrt{1^2 + 2^2} = \sqrt{5}$. So, $\mathbf{u} = \frac{\mathbf{a}}{|\mathbf{a}|} = \frac{1}{\sqrt{5}}\mathbf{i} + \frac{2}{\sqrt{5}}\mathbf{j}$.
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