The cauchy schwartz inequality for any two vectors \(\vec{a}\) and \(\vec{b}\) is

\(\left|\vec{a}\cdot \vec{b}\right|=\left|\vec{a}\right|\left|\vec{b}\right|\) \(\left|\vec{a}\cdot \vec{b}\right|\leq\left|\vec{a}\right|\left|\vec{b}\right|\) \(\left|\vec{a}\cdot \vec{b}\right|\geq \left|\vec{a}\right|\left|\vec{b}\right|\) \(\left|\vec{a}+ \vec{b}\right|\leq \left|\vec{a}\right| + \left|\vec{b}\right|\)

\(\left|\vec{a}\cdot \vec{b}\right|\leq\left|\vec{a}\right|\left|\vec{b}\right|\)

Recall cauchy schwartz inequality