An unknown in a sum of three vectors

It is given that \(\mathbf{p}=\begin{pmatrix}2\\ -5\end{pmatrix}\), \(\mathbf{q}=\begin{pmatrix}-4\\ 3\end{pmatrix}\) and \(\mathbf{r}=\begin{pmatrix}k\\ 6\end{pmatrix}\).

1. Given that \(\mathbf{p}+\mathbf{q}+\mathbf{r}=\begin{pmatrix}1\\ 4\end{pmatrix}\), find \(k\).[2]
2. Find \(|\mathbf{p}+\mathbf{q}|\), leaving your answer in surd form.[2]