\( \begin{array}{l} (\left| {\overrightarrow a + \overrightarrow b } \right|)^2 - (\left| {\overrightarrow a - \overrightarrow b } \right|)^2 = a^2 + b^2 + 2\overrightarrow a .\overrightarrow b - a^2 - b^2 + 2\overrightarrow a .\overrightarrow b = 4\overrightarrow a .\overrightarrow b = 5^2 - 3^2 \\ = > \overrightarrow a .\overrightarrow b = 4 \\ \end{array} \)
