I would like to ask how to find a normal vector $\gamma$ for a separating or supporting hyperplane for the following sets $A$ and points $d$:
$1.\quad A=\{(x,y):x\ge 0,y \ge 0\}$ and $d=(-1,-1)$
$2.\quad A=\{(x,y,z):x^{2}+y^{2}+z^{2}\le 9\}$ and $d=(3,0,0)$
Hint is to draw a picture, but I still don't understand how I know according to the picture that the answer is:
$1.\quad \gamma=(-1,-1)$ or $\gamma=(1,1)$
$2.\quad \gamma=(1,0,0)$ or $\gamma=(-1,0,0)$
Could you help me? Thanks.