If $\mathbf{a} = \mathbf{i} + 3 \mathbf{j} + \mathbf{k}$ and $\mathbf{b} = \mathbf{i} + 9 \mathbf{j} + \mathbf{k}$, find a unit vector with positive first coordinate orthogonal to both $\mathbf{a}$ and $\mathbf{b}$.
$\mathbf{i}$ + $\mathbf{j}$ + $\mathbf{k}$