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

Answer: (B)

$|\vec{a}|=8,|\vec{b}|=7,|\vec{c}|=10$
$\cos \theta =\frac{|\vec{b}{|}^2+|\vec{c}{|}^2-|\vec{a}{|}^2}{2|\vec{b}||\vec{c}|}=\frac{17}{28}$
Projection of $\vec{c}$ on $\vec{b}$
$=|\vec{c}|\cos \theta$
$=10\times \frac{17}{28}$
$=\frac{85}{14}$