Question

A particle moves from the position $\overrightarrow{r_1}=3\hat{i}+2\hat{j}-6\hat{k}$ to position $\overrightarrow{r_2}=14\hat{i}+13\hat{j}+9\hat{k}$ under the action of a force $\overrightarrow{F}=4\hat{i}+\hat{j}+3\hat{k}$. The work done by the force is

• A. 50 units
• B. 75 units
• C. 100 units
• D. 200 units

Answer 1

The correct option is C 100 units

$\overrightarrow{r}=\overrightarrow{r_2}-\overrightarrow{r_1}=(11\hat{i}+11\hat{j}+15\hat{k})$
Work done $=\overrightarrow{F}\cdot \overrightarrow{r}=44+11+45=100$ units