\text { Suppose } \vec{b} \text { is a linear combination of the vectors }\left(\begin{array}{l} 3 \\ 0 \\ 9 \\ 4 \end{array}\right),\left(\begin{array}{l} 2 \\ 1 \\ 6 \\ 8

\end{array}\right),\left(\begin{array}{c} 4 \\ -3 \\ 12 \\ 10 \end{array}\right), \text { and }\left(\begin{array}{c} 1 \\ 8 \\ 3 \\ -7 \end{array}\right) . \text { If the first element of } \vec{b} \text { is } 5, \text { find the third element of } \vec{b} \text { . }