Intuition of convex set separation hyper-plane

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According to the hyperplane separation theorem

Let A and B be two disjoint nonempty convex subsets of Rn. Then there exists a non-zero vector v and a real number c such that

$$ <x,v> \le c $$ and $$<y,v> \ge c $$

for all x in A and y in B; i.e., the hyperplane $$ <.,v> = c $$, v the normal vector, separates A and B

I am facing difficulties to understand what is the meaning of <.,v> and how does it represent hyperplane.

Appreciate your insights.