Question

Find the angle between force $F=(3\hat{i}+4\hat{j}-5\hat{k})$ unit and displacement $d=(5\hat{i}+4\hat{j}+3\hat{k})$ unit. Also find the projection of $F$ and $d$.

Answer 1

Here,

$\overrightarrow{F}=3\hat{i}+4\hat{j}-5\hat{k}$

$d=5\hat{i}+4\hat{j}+3\hat{k}$

$\overrightarrow{F}.d=15+16-15=16$

$\left|F\right|=\sqrt{50}$

$\left|d\right|=\sqrt{50}$

$\cos \theta =\frac{F.d}{\left|F\right|\left|d\right|}$

$\theta ={\cos }^{-}\left(\frac{16}{50}\right)$

$\theta ={\cos }^{-}\left(0.32\right)$

$\overrightarrow{F}ond=\overrightarrow{F}\cos \theta$

$=\sqrt{50}\frac{16}{\sqrt{50}}$

$=16$