The Reimer-Tiemann reaction involves the electrophilic substitution of phenol with chloroform to form substituted benzal chloride.
If $ | \vec{a} | = 3 $, $ | \vec{b} | = 2 $, then find $ (3\vec{a} - 2\vec{b}) \cdot (3\vec{a} + 2\vec{b}) $.