# Minkowski sum and vectors

Problem:

Given two convex polygons A, B, we can define Minkowski sum, as A + B = {a + b: a $\in$ A, b $\in$ B}, where a + b vector sum. Prove that:

for every external perpendicular u to an edge of A, there exists an external perpendicular to an edge of A + B, which will be parallel to u.

Attempt:

I know that the external perpendicular has maximum inner product for points that lie in that edge of the polygon, i.e. = max <=> p $\in$ edge.

So now, I assume I have an edge a of A and $\overline{b}$ = {b $\in$ B | $u^T$ to be max}.