The vectors $\mathbf{a}$ and $\mathbf{b}$ are given by $\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}$ and $\mathbf{b} = -\mathbf{i} + 4\mathbf{j}$. (a) Find $\mathbf{a} + \mathbf{b}$ and $2\mathbf{a} - \mathbf{b}$. (4 marks) (b) Find $|\mathbf{a}|$ and hence a unit vector in the direction of $\mathbf{a}$. (4 marks) (c) Find the scalar product $\mathbf{a} \cdot \mathbf{b}$ and hence the angle between $\mathbf{a}$ and $\mathbf{b}$, correct to one decimal place. (7 marks)