Let v_{1} = \left [ \begin{matrix} 6 \\ 2 \\ 2 \end{matrix} \right ] , v_{2} = \left [ \begin{matrix} 7 \\ 1 \\ 5 \end{matrix} \right ] , v_{3} = \left [ \begin{matrix} -2 \\ 4 \\ -1 \end{matrix} \right ] , p_{1} = \left [ \begin{matrix} 1 \\ 3 \\ 1 \end{matrix} \right ] , \text{and} p_{2} = \left [ \begin{matrix} 3 \\ 2 \\ 1 \end{matrix} \right ] , \text{and let} S = \{v_{1},v_{2},v_{3}\} . Determine whether p_{1} and p_{2} are in conv S.