Question

If forces of magnitudes $6$ and $7$ units acting in the directions $\hat{i}-2\hat{j}+2\hat{k}$ and $2\hat{i}-3\hat{j}-6\hat{k}$ respectively act on a particle which is displaced from the point $P(2,-1,-3)$ to $Q(5,-1,1)$ , then the work done by the forces is

• A. $4$ units
• B. $-4$ units
• C. $7$ units
• D. $-7$ units

Answer 1

The correct option is A $4$ units

Resultatnt is given by

$\overline{r}=(3,0,4)$

${\overline{F}}_r=2(\overline{i}-2\overline{j}+2\overline{k})+2\overline{i}-3\overline{j}-6\overline{k}$
$=4\overline{i}-7\overline{j}-2\overline{k}$

$W={\overline{F}}_r\cdot \overline{r}$
$=12-8$
$=4$ units