Vectors - Angles Between Vectors

Given \(\left| \mathbf{a} \right|=7\) and \(\left| \mathbf{b} \right|=4\), \(\mathbf{a}\cdot \mathbf{b}=8\).

1. Calculate the angle between vectors \(\mathbf{a}\) and \(\mathbf{b}\).
2. Find the values of \((\mathbf{a}+\mathbf{b})\cdot (\mathbf{a}+\mathbf{b})\) and \((\mathbf{a}-\mathbf{b})\cdot (\mathbf{a}-\mathbf{b})\).
3. Hence, find the values of \(\left| \mathbf{a}+\mathbf{b} \right|\) and \(\left| \mathbf{a}-\mathbf{b} \right|\).