Vectors - Vector (Cross) Product

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