I need to create Convex Hull using QuickHull algorithm so I need to find two point for which x is smallest and largest and I need to check if the 3rd point is below or above. When I have points that are in $R^2$ I can detect if it's below of above line by creating function based on two points:
$ f(x) = \frac{y_2 - y_1}{x_2 - x_1} (x-x_1)+y_1 $
and then I can check if:
$ f(x_3) < y_3 $
How can I do the same but for $x \in R^3$ and $x \in R^n$?