If \(|\vec{a}+\vec{b}|=|\vec{a}|+|\vec{b}|\) where \(\vec{a}\) and \(\vec{b}\) are any vectots, then this equality

always holds never holds holds only when \(\vec{a}=k\vec{b}\) or one of \(\vec{a}\) and \(\vec{b}\) is zero holds only \(\vec{a}=\vec{b}=0\)

holds only when \(\vec{a}=k\vec{b}\) or one of \(\vec{a}\) and \(\vec{b}\) is zero

\(|\vec{A}+\vec{b}|=|\vec{a}|+|\vec{b}|\) thus \(\vec{a}\) and \(\vec{b}\) are scalar multiple of each other so \(\vec{a}=k\vec{b}\)