Question

A small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} N$. The value of work done will be ________$J$.

Answer 1

$ W=\vec{F} \cdot\left(\vec{r}_f-\vec{r}_{ i }\right) $
$ =(5 \hat{i}+2 \hat{j}+7 \hat{k}) \cdot((5 \hat{i}-2 \hat{j}+\hat{k})-(2 \hat{i}+3 \hat{j}-4 \hat{k}))$
$ W=40 \,J$