In a triangle ABC,


In a triangle $\mathrm{ABC}$, if $|\overrightarrow{\mathrm{BC}}|=8,|\overrightarrow{\mathrm{CA}}|=7$,

$|\overrightarrow{\mathrm{AB}}|=10$, then the projection of the vector $\overrightarrow{\mathrm{AB}}$ on $\overrightarrow{\mathrm{AC}}$ is equal to:

  1. $\frac{25}{4}$

  2. $\frac{85}{14}$

  3. $\frac{127}{20}$

  4. $\frac{115}{16}$

Correct Option: , 2



$\cos \theta=\frac{|\vec{b}|^{2}+|\vec{c}|^{2}-|\vec{a}|^{2}}{2|\vec{b}||\vec{c}|}=\frac{17}{28}$

Projection of $\vec{c}$ on $\vec{b}$

$=|\vec{c}| \cos \theta$

$=10 \times \frac{17}{28}$



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