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 $F$ on $d$.

Answer 1

$\overrightarrow{F}.\overrightarrow{d}=Fd\cos \theta$

$⟹\cos \theta =\frac{\overrightarrow{F}.\overrightarrow{d}}{Fd}=\frac{15+16+15}{50}=\frac{46}{50}$

$⟹\theta ={\cos }^{-1}0.92$

Projection of $\overrightarrow{F}$ on $\overrightarrow{d}$ is given by

$\frac{\overrightarrow{F}.\overrightarrow{d}}{d}$

$=\frac{15+16+15}{\sqrt{5^2+4^2+3^2}}$

$=\frac{46}{5\sqrt{2}}$