MathNet 2021 — Part 02 Question 65

Given vectors $\vec{a} = (1 + 2^m, 1 - 2^m)$, $\vec{b} = (4^m - 3, 4^m + 5)$, suppose $m$ is real. Then the minimum of the dot product of $\vec{a} \cdot \vec{b}$ is ______.