Mathematics - Vector Question with Solution | TestHub

We have,

$\left|\overrightarrow{a}\right|=3,\left|\overrightarrow{b}\right|=5,\left|\overrightarrow{c}\right|=7$

Now,

$\cos \theta =\frac{{\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{c}\right|}^2-{\left|\overrightarrow{b}\right|}^2}{2\left|\overrightarrow{a}\right|\left|\overrightarrow{c}\right|}$

$\Rightarrow \cos \theta =\frac{9+49-25}{2·3·7}$

$\Rightarrow \cos \theta =\frac{11}{14}$

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

$=\left|\overrightarrow{c}\right|\cos \theta$

$=7\times \frac{11}{14}$

$=\frac{11}{2}$