If $\overline{\mathrm{a}},\overline{\mathrm{b}},\overline{\mathrm{c}}$ are vectors and $\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}\text{ and }\left|\overline{\mathrm{a}}\right|=7,\left|\overline{\mathrm{b}}\right|=5,\left|\mathrm{c}\right|=3$ then angle between vector $\overline{\mathrm{b}} \mathrm{and} \overline{\mathrm{c}}$ is 

$\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}\Rightarrow \overline{\mathrm{b}}+\overline{\mathrm{c}}=-\overline{\mathrm{a}}$ s.o.bs
$\begin{array}{l}(\overline{\mathrm{b}}+\overline{\mathrm{c}}{)}^2=|\overline{\mathrm{a}}{|}^2\Rightarrow |\overline{\mathrm{b}}{|}^2+|\overline{\mathrm{c}}{|}^2+2\left(\right|\mathrm{b}\left|\right|\mathrm{c}|\cos (\overline{\mathrm{b}},\overline{\mathrm{c}}\left)\right)\Rightarrow |\overline{\mathrm{a}}{|}^2=25+9+2(5\cdot 3\cdot \cos (\overline{\mathrm{b}},\overline{\mathrm{c}}))=49\\ 30\cos (\overline{\mathrm{b}},\overline{\mathrm{c}})=49-9-25\Rightarrow \cos (\overline{\mathrm{b}},\overline{\mathrm{c}})=\frac{1}{2},\therefore (\overline{\mathrm{b}},\overline{\mathrm{c}})={60}^{\circ }\end{array}$