2024 EJC Promo Q5

\(\mathbf{a}\) and \(\mathbf{b}\) are vectors such that \(|\mathbf{a}| = \sqrt{2}\) and \(|\mathbf{b}| = \sqrt{6}\). The angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(\frac{5\pi}{6}\).

1. Find the exact length of projection of \(\mathbf{a}\) onto \(\mathbf{b}\).[2]
2. By considering \((3\mathbf{a} + 2\mathbf{b}) \cdot (3\mathbf{a} + 2\mathbf{b})\), find the exact value of \(|3\mathbf{a} + 2\mathbf{b}|\).[4]