Let a_{1} = \left [ \begin{matrix} 2 \\ 1 \\ 1 \end{matrix} \right ] , a_{2} = \left [ \begin{matrix} -3 \\ 2 \\ 1 \end{matrix} \right ] , a_{3} = \left [ \begin{matrix} 3 \\ 4 \\ 0 \end{matrix} \right ] , b_{1} = \left [ \begin{matrix} 1 \\ 0 \\ 2 \end{matrix} \right ] , \text{and} b_{2} = \left [ \begin{matrix} 2 \\ -1 \\ 5 \end{matrix} \right ] , and let A = \{a_{1} , a_{2} , a_{3}\} and B = \{b_{1} , b_{2}\} . Show that the hyperplane H = [f:5] , where f(x_{1},x_{2},x_{3}) = 2x_{1} - 3x_{2} + x_{3} , does not separate A and B. Is there a hyperplane parallel to H that does separate A and B? Do the convex hulls of A and B intersect?