Mathematics

Problem

15. Prove that

(\vec{a}+\vec{b}) \cdot(\vec{a}+\vec{b})=|\vec{a}|^{2}+|\vec{b}|^{2}

, if and only if

\vec{a}, \vec{b}

are perpendicular, given

\vec{a} \neq \overrightarrow{0}, \vec{b} \neq \overrightarrow{0}