Q:

Equation of Plane through Center

I have a pentagon for which 3 vertices were chosen to compute the equation of the plane. How to I find the normal passing through its center?
$$P_1 =  [ 3.096, \ 0.492, \  3.287]$$
$$P_2 =  [ 3.118, \ 0.227, \ 4.669]$$
$$P_3 = [ 2.214, \ 1.476, \ 2.801]$$
Equation of Plane: 
$$ 2.809x + 0.732y - 3.586z = 4.614 $$
Given this equation how do I find the normal passing through the center of the pentagon?

A:

HINT

from the equation of the plane $ax+by+cz=d$ we know that $n=(a,b,c)$
find $P_4$ and $P_5$ by vectors
the center of the pentagon is given by $C=\frac{P_1+P_2+P_3+P_4+P_5}5$

