Vectors - Angles Between Vectors

Given two vectors \(\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}\) and \(\mathbf{b}=3\mathbf{i}+4\mathbf{j}-\mathbf{k}\), find:

1. a unit vector perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\).
2. the exact value of \(\sin\theta\), where \(\theta\) is the angle between \(\mathbf{a}\) and \(\mathbf{b}\).