We can do this by adding the corresponding components of each vector. So, we have:
$$
\mathbf{u} + \mathbf{v} = (1 + 0)\mathbf{i} + (1 - 1)\mathbf{j} + (0 - 2)\mathbf{k} = \mathbf{i} - 2\mathbf{k}
$$
So, $\mathbf{u} + \mathbf{v} = <1,0,-2>$.
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