1.1.16 Vector Algebra

Problem: Calculate the area of the parallelogram formed by the vectors \( \vec{a} \) and \( \vec{b} \). \[ \begin{array}{l} \vec{a}=3 \vec{p}+\vec{q}, \quad \vec{b}=\vec{p}-3 \vec{q}, \quad|\vec{p}|=7, \\ |\vec{q}|=2, \quad(\widehat{\vec{p} ; \vec{q}})=\frac{\pi}{4} . \end{array} \]