In a triangle ABC, if $\left|\overrightarrow{\mathrm{BC}}\right|=3, \left|\overrightarrow{\mathrm{CA}}\right|=5, \left|\overrightarrow{\mathrm{BA}}\right|=7,,$then the projection of the vector $\overrightarrow{\mathrm{BA}} \mathrm{on} \overrightarrow{\mathrm{BC}}$ is equal to :

$$\begin{gathered} \mathrm{a}=\left|\overline{\mathrm{BC}}\right|=3 \mathrm{b}=\left|\overline{\mathrm{CA}}\right|=5 \mathrm{c}=\left|\overline{\mathrm{BA}}\right|=7 \\ \cos \mathrm{B}=\frac{{\mathrm{a}}^2+{\mathrm{c}}^2-{\mathrm{b}}^2}{2\mathrm{ac}}=\frac{9+49-25}{2\times 3\times 7}=\frac{33}{14\times 3}=\frac{11}{14} \\ \mathrm{Proj} \overline{\mathrm{BA}} \mathrm{or} \overline{\mathrm{BC}}=\frac{\overline{\mathrm{BA}}.\overline{\mathrm{BC}}}{\left|\overline{\mathrm{BC}}\right|}=\left|\overline{\mathrm{BA}}\right|\cos \mathrm{B} \\ =7\times \frac{11}{14}=\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \end{gathered}$$