Question

Constant forces $\overline{p_1}=\hat{i}-\hat{j}+\hat{k},\overline{p_2}=\hat{i}+2\hat{j}-\hat{k}$ and $\overline{p_3}=\hat{j}-\hat{k}$ act on a particle at the point $A$. Determine the work done when the particle is displaced from the point $A$ to $B$ where $\overline{OA}=4\hat{i}-3\hat{j}-2\hat{k}$ and $\overline{OB}=6\hat{i}-\hat{j}-3\hat{k}$ are the position vectors of $A$ and $B$, is

• A. $4$
• B. $19$
• C. $9$
• D. $7$

Answer 1

The correct option is C $9$

Resultant force at $A$ $\overline{p}=\overline{p_1}+\overline{p_2}+\overline{p_3}$

$=2\hat{j}-\hat{k}$

$\overline{AB}=\overline{OB}-\overline{OA}=2\hat{i}+4\hat{j}-\hat{k}$

$\therefore$ Work done $=\overline{p}\cdot \overline{AB}=(2\hat{j}-\hat{k})\cdot (2\hat{i}+4\hat{j}-\hat{k})$

$=0+8+1$

$=9$ units.