If $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ and the angle between $\overrightarrow{A}\text{and}\overrightarrow{B}$ is$120°$ , then the magnitude of$\overrightarrow{C}$   

$\left|\overrightarrow{A}+\overrightarrow{B}\right|=\left|\overrightarrow{C}\right|\text{S}\text{.O}\text{.B}\text{.S}$

$\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}+2\text{AB}\cos \theta }=C$

$\text{C}=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}+2\text{AB}\cos 120°}$

$=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}+2\text{AB}\left(-\frac{1}{2}\right)}$

$=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}-\text{AB}}$                                             $\left|\overrightarrow{A}+\overrightarrow{B}\right|<\left|\overrightarrow{A}-\overrightarrow{B}\right|$

$\left|\overrightarrow{A}-\overrightarrow{B}\right|=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}-2\text{AB}\cos 120°}$                  $\text{if }\theta =120°\text{b/w }\overrightarrow{A}\&\overrightarrow{B}$

$=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}-2\text{AB}\left(-\frac{1}{2}\right)}$

$=\sqrt{{\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}+\text{AB}}$