3. (5+4+6-15 pts.) Let a₁ = -8-0-0-0-0-0 , Let A (a1, a2, as), B = (b, by, bs), S conv (a1, a2, as) and T = conv (b₁, b₂, ba}- and n = (a) Find a hyperplane H with normal n that separates A and B. (b) Is there a hyperplane parallel to H that strictly separates A and B (e) Find the maximum and minimum of the linear functional f(#1, #2, #3)=3x+22-23 on S and T respectively and indicate at which x these maximum and minimum are attained.