Chapter 8.4, Problem 12E

Let ${\text{a}}_1=\left[\begin{array}{c}2\\ -1\\ 5\end{array}\right]$, ${\text{a}}_2=\left[\begin{array}{c}3\\ 1\\ 3\end{array}\right]$, ${\text{a}}_3=\left[\begin{array}{c}-1\\ 6\\ 0\end{array}\right]$, ${\text{b}}_1=\left[\begin{array}{c}0\\ 5\\ -1\end{array}\right]$, ${\text{b}}_2=\left[\begin{array}{c}1\\ -3\\ -2\end{array}\right]$, ${\text{b}}_3=\left[\begin{array}{c}2\\ 2\\ 1\end{array}\right]$ and $\text{n}=\left[\begin{array}{c}3\\ 1\\ -2\end{array}\right]$, and let A = {a₁, a₂, a₃} and B = {b₁, b₂, b₃}. Find a hyperplane H with normal n that separates A and B. Is there a hyperplane parallel to H that strictly separates A and B?