Question

Forces acting on a particle have magnitudes of 14, 7, and 7 N and act in the direction of vectors $6\hat{i}+2\hat{j}+3\hat{k},3\hat{i}-2\hat{j}+6\hat{k},2\hat{i}-3\hat{j}-6\hat{k}$ respectively. The forces remain constant while the particle is displaced from point A: (2, 1, -3) to B: (5, 1, 1). Find the work done. The coordinates are specified in meters.

• A. $75J$
• B. $55J$
• C. $85J$
• D. $65J$

Answer 1

The correct option is A $75J$

The magnitude of each of the three vectors is 7. We divide each of the magnitude 14, 7 and 7 by 7.

Thus, we multiply the given vectors by 2, 1 and 1 respectively.

$W=\overrightarrow{F}.\overrightarrow{d},\overrightarrow{d}=(3\hat{i}+4\hat{k}),\overrightarrow{F}=(12\hat{i}+4\hat{j}+6\hat{k})+(3\hat{i}-2\hat{j}+6\hat{k})+(2\hat{i}-3\hat{j}-6\hat{k})=(17\hat{i}-\hat{j}+6\hat{k})\Rightarrow W=\overrightarrow{F.}\overrightarrow{d}=51+24=75J$