A particle moves from a point $(-2 \hat{i}+5 \hat{j})$ to $(4 \hat{j}+3 \hat{k})$ when a force of $(

Question

A particle moves from a point $(-2 \hat{i}+5 \hat{j})$ to $(4 \hat{j}+3 \hat{k})$ when a force of $(4 \hat{i}+3 \hat{j}) \mathrm{N}$ is applied. How much work has been done by the force?\

Professor PC Thomas Classes · Answer

(c) : Here $\vec{r}_{1}=(-2 \hat{i}+5 \hat{j}) \mathrm{m}, \vec{r}_{2}=(4 \hat{j}+3 \hat{k}) \mathrm{m}$ $$ \vec{F}=(4 \hat{i}+3 \hat{j}) \mathrm{N}, W=? $$ Work done by force $F$ in moving from $\vec{r}_{1}$ to $\vec{r}_{2}$,\ $W=\vec{F} \cdot\left(\vec{r}_{2}-\vec{r}_{1}ight) \Rightarrow W=(4 \hat{i}+3 \hat{j}) \cdot(4 \hat{j}+3 \hat{k}+2 \hat{i}-5 \hat{j})$ $$ =(4 \hat{i}+3 \hat{j}) \cdot(2 \hat{i}-\hat{j}+3 \hat{k})=8+(-3)=5 \mathrm{~J} $$