\(|\vec{R}|=|\vec{A}+\vec{B}|=\sqrt{A^2+B^2+2 A B \cos \theta}\)

\(|\vec{A}|=|\vec{B}|=|\vec{R}|=1\)

\(1=1+1+2 \times 1 \times 1 \times \cos \theta\)

\(\cos \theta=-\frac{1}{2} \Rightarrow \theta=120^{\circ}\)

\(|\vec{R}|=|\vec{A}-\vec{B}|=\sqrt{A^2+B^2-2 A B \cos 120^{\circ}}\)

\(=\sqrt{1^2+1^2-2 \times 1 \times 1 \times\left(-\frac{1}{2}\right)}=\sqrt{3}=|\vec{A}-\vec{B}|\)