Physics - W.E.P. Question with Solution | TestHub

Initial position vector, ${\vec{r}}_1=3\hat{i}+2\hat{j}-6\hat{k}$

Final position vector, ${\vec{r}}_2=14\hat{i}+13\hat{j}+9\hat{k}$

Displacement vector, $\vec{s}={\vec{r}}_2-{\vec{r}}_1$

$\vec{s}=(14-3)\hat{i}+(13-2)\hat{j}+(9-(-6))\hat{k}$

$\vec{s}=11\hat{i}+11\hat{j}+15\hat{k}$

Force vector, $\vec{F}=4\hat{i}+\hat{j}+3\hat{k}$

Work done, $W=\vec{F}\cdot \vec{s}$

$W=(4\hat{i}+\hat{j}+3\hat{k})\cdot (11\hat{i}+11\hat{j}+15\hat{k})$

$W=(4\times 11)+(1\times 11)+(3\times 15)$

$W=44+11+45=100$ J

Answer: $100$ J