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\((\vec{a} + \vec{b}).(\vec{a} + \vec{b}) = |\vec{a}|^2 + |\vec{b}|^2\) if and only if  \(\vec{a},\; \vec{b}\) are perpendicular givens \(\vec{a} \neq \vec{0},\; \vec{b}\neq\vec{0}\)

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

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