Ans: (D)
\(|\vec{a}+\vec{b}|<|\vec{a}-\vec{b}| \Rightarrow|\vec{a}+\vec{b}|^{2}<|\vec{a}-\vec{b}|^{2}\)
\(|\vec{a}|^{2}+|\vec{b}|+2|\vec{a}||\vec{b}| \cos \alpha<|\vec{a}|^{2}+|\vec{b}|-2|\vec{a}||\vec{b}| \cos \alpha\), (where \(\alpha\) is an angle between \(\vec{a}\) and \(\vec{b}\) vector
\(\Rightarrow 4|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \cos \alpha<0, \Rightarrow \cos \alpha<0, \Rightarrow \alpha\) is an obtuse angle
