Change color of overlapping convex hull and original function

Question

I am trying to demonstrate how the convex hull for my function and using the following formula for that (where the first inequality is the original function, and the second one is its convexified version):

RegionPlot3D[{(2 v1 v2 v3)/(v1 v2 + v2 v3 + v1 v3) < v3, 0.75 v1 + 0.75 v2 - 2.25 v3 - 1.125 < 0}, {v1, 1, 3}, {v2, 1, 3}, {v3, 1, 3}, ViewPoint -> {2, 1.0, -1.1}, BoundaryStyle -> Directive[Black], MeshFunctions -> {#3 &  }]

The result looks as follows:

Note that the "left" intersection of the set is highlighted with orange, while the "right" one is highlighted with blue. It is possible somehow to prioritize the color of the first function for the intersections, i.e., the only blue part would be the triangle "at the bottom"?

Answer 1

Clear[reg, reg1];
reg = ImplicitRegion[(2 v1 v2 v3)/(v1 v2 + v2 v3 + v1 v3) < 
    v3, {{v1, 1, 3}, {v2, 1, 3}, {v3, 1, 3}}];
reg1 = RegionDifference[ConvexHullRegion[reg], reg];
Show[RegionPlot3D[reg, MeshFunctions -> {#3 &}, Mesh -> Automatic], 
 Region[Style[reg1, Blue]], ViewPoint -> {2, 1.0, -1.1}, 
 Boxed -> False]