\(\vec{c}\) cùng phương \(\vec{a}\) và \(|\vec{c}|=3 \sqrt{5} \Leftrightarrow\left\{\begin{array}{l}\frac{m+n}{1}=\frac{-m-4 n}{-2} \\ \sqrt{(m+n)^{2}+(-m-4 n)^{2}}=3 \sqrt{5}\end{array}\right.\)

\(\Leftrightarrow\left\{\begin{array}{l}-2 m-2 n=-m-4 n \\ (m+n)^{2}+(m+4 n)^{2}=45\end{array} \Leftrightarrow\left\{\begin{array}{l}m=2 n \\ (3 n)^{2}+(6 n)^{2}=45\end{array} \Leftrightarrow\left\{\begin{array}{l}m=2 n \\ (3 n)^{2}+(6 n)^{2}=45\end{array}\right.\right.\right.\)

\(\Leftrightarrow\left\{\begin{array}{l}m=2 n \\ 45 n^{2}=45\end{array} \Leftrightarrow\left\{\begin{array}{l}m=2 \\ n=1\end{array} \vee\left\{\begin{array}{l}m=-2 \\ n=-1\end{array}\right.\right.\right.\).