A body constrained to move along the z-axis of a coordinate system is subject to a constant force $F$ given by $F=-\hat{i}+2 \hat{j}+3 \hat{k} \mathrm{~N}$ where i, $\mathbf{j}, \mathrm{k}$, are unit vectors along the $\mathrm{x}-\mathrm{y}$ – and $z$-axis of the system respectively. What is the work done by this force in moving the body at a distance of $4 \mathrm{~m}$ along the z-axis?
The body is displaced by $4 \mathrm{~m}$ along $z$-axis, so we have,
$\vec{S}=0 \hat{i}+0 \hat{j}+4 \hat{k}$
$\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}$
Work done can be calculated as,
$W=\vec{F} \cdot \vec{S}=(0 \hat{i}+0 \hat{j}+4 \hat{k})(-\hat{i}+2 \hat{j}+3 \hat{k})$
$=12(\hat{k} \cdot \hat{k})$ Joule $=12$ Joule
