Where do these vector equations indicate? Above or Below?

Question

I am a little confused. I have seen different notation in different papers. Let me ask clearly:

Assume points A1 and A2 on the 2D plan. Point Z lies on the line between A1 and A2. Dashed lined is a perpendicular line, L, to point Z. Assume f is any point on the plane, f=(f1,f2);

what does equation 1 and 2 gives? Do they both indicates the area above the grey line? If possible please explain why!

P.S. My best guess is, Equation 1 indicates the points above the line L and Equation 2 indicates the area below line L.

U= A2-A1;  % Black 
V=A1-A2;   % Red 
f= (f1,f2) % any point
U.(f-Z)<0  % Equation 1
V.(f-Z)<0  % Equation

Answer 1

$U \circ (f-Z)$ is the set of all points f that lie on one side of the line L, the side that contains the point A1. The other equation gives the other side, the one that contains A2.

Why? $f-Z$ is a vector pointing from Z to f. But if $u$ is the unit vector along $U$, $u \circ (f-Z)$ is the component of $f-Z$ that is along U. For that component to be negative, f must be on the A1 side of L. Of course, $$u \circ (f-Z) <0 \Longleftrightarrow U \circ (f-Z)$$.