Q: A body is displaced from $ \vec{r_A} = ( 2\hat{i} + 4 \hat{j} – 6\hat{k} ) $ to $ \vec{r_B} = ( 6\hat{i} – 4 \hat{j} + 2\hat{k}) $ under a constant force $ \vec{F} = (2\hat{i} + 3 \hat{j} – \hat{k}) $ . Find the work done.

Sol: Work done $\large W = \vec{F}.\vec{S}$

$\large W = \vec{F}.(\vec{r_B}-\vec{r_A}) $

$\large W = (2\hat{i} + 3 \hat{j} – \hat{k}).(( 6\hat{i} – 4 \hat{j} + 2\hat{k})-( 2\hat{i} + 4 \hat{j} – 6\hat{k} )) $

$\large = (2\hat{i} + 3 \hat{j} – \hat{k}).(4\hat{i} – 8\hat{j}+ 8\hat{k})$

W = 8 -24 -8 = -24 units