In a triangle ABC,


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

  1. $\frac{19}{2}$

  2. $\frac{13}{2}$

  3. $\frac{11}{2}$

  4. $\frac{15}{2}$

Correct Option: , 3


Projection of $\overrightarrow{\mathrm{BA}}$

on $\overrightarrow{\mathrm{BC}}$ is equal to

$=|\mathrm{BA} \overrightarrow{\mathrm{A}}| \cos \angle \mathrm{ABC}$

$=7\left|\frac{7^{2}+3^{2}-5^{2}}{2 \times 7 \times 3}\right|=\frac{11}{2}$

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