Question:
A particle moves from a point $r=(2 \mathrm{~m})^{\hat{\imath}}+(3 \mathrm{~m})^{\hat{\jmath}}$ to another point $r_{2}=(3 \mathrm{~m})^{\hat{\imath}}+(2 \mathrm{~m})^{\hat{\jmath}}$ during which a certain force $F=(5 \mathrm{~N})^{\hat{l}}+(5 \mathrm{~N})^{\hat{J}}$ acts on it. Find the work done by the force on the particle during the displacement.
Solution:
$r=r_{2}-r_{1}$
$=\left(3^{\hat{2}}+2^{\hat{j}}\right)-\left(2^{\hat{2}}+3^{\hat{j}}\right)$
$r=\hat{\imath}_{-} \hat{\jmath}$
Work done $\mathrm{W}=\mathrm{F} \times \mathrm{r}$
$W=\left(5^{\hat{\imath}}+5^{\hat{\jmath}}\right) \times\left({ }^{\hat{\imath}}-\hat{\jmath}\right)$
$W=0$