Question

In a triangle $ABC,$ if $|\overrightarrow{BC}|=8,|\overrightarrow{CA}|=7,|\overrightarrow{AB}|=10$, then the projection of the vector $\overrightarrow{AB}$ on $\overrightarrow{AC}$ is equal to:

• A. $\frac{25}{4}$
• B. $\frac{85}{14}$
• C. $\frac{127}{20}$
• D. $\frac{115}{16}$

Answer 1

The correct option is B $\frac{85}{14}$


Projection of $AB$ on $AC$
$=AB\cos A=10\cos A$

By cosine rule,
$\cos A=\frac{{10}^2+7^2-8^2}{2\cdot 10\cdot 7}\Rightarrow \cos A=\frac{17}{28}$
Therefore,
$10\cos A=10\times \frac{17}{28}=\frac{85}{14}$