For two non-zero vectors $\displaystyle \vec{\mathrm{a}}$ and $\displaystyle \vec{\mathrm{b}}$, if $\displaystyle |\vec{\mathrm{a}}-\vec{\mathrm{b}}|=|\vec{\mathrm{a}}+\vec{\mathrm{b}}|$, then find the angle between $\displaystyle \overrightarrow{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{b}}$.

$$\begin{aligned} & |\vec{\mathrm{a}}-\vec{\mathrm{b}}|^{2}=|\vec{\mathrm{a}}+\vec{\mathrm{b}}|^{2} \\ & \Rightarrow|\vec{\mathrm{a}}|^{2}-2 \vec{\mathrm{a}} \cdot \vec{\mathrm{b}}+|\vec{\mathrm{b}}|^{2}=|\vec{\mathrm{a}}|^{2}+2 \vec{\mathrm{a}} \cdot \vec{\mathrm{b}}+|\vec{\mathrm{b}}|^{2} \\ & \Rightarrow 4 \vec{\mathrm{a}} \cdot \vec{\mathrm{b}}=0 \\ & \Rightarrow \text { angle between } \overrightarrow{\mathrm{a}} \text { and } \overrightarrow{\mathrm{b}} \text { is } 90^{\circ} \end{aligned} $$