Let v_{1} = \left [ \begin{matrix} 3 \\ 0 \\ 6 \\ -3 \end{matrix} \right ] , v_{2} = \left [ \begin{matrix} -6 \\ 3 \\ 3 \\ 0 \end{matrix} \right ] , v_{3} = \left [ \begin{matrix} 3 \\ 6 \\ 0 \\ 3 \end{matrix} \right ] , p_{1} = \left [ \begin{matrix} 0 \\ 3 \\ 3 \\ 0 \end{matrix} \right ] , p_{2} = \left [ \begin{matrix} -10 \\ 5 \\ 11 \\ -4 \end{matrix} \right ] , and S = \{v_{1},v_{2},v_{3}\} . Note that S is an orthogonal set. Determine whether p_{1} is in Span S, aff S, and conv S. Then do the same for p_{2} .