Question

The work done by a force $\overrightarrow{F}=3\hat{i}-4\hat{j}+5\hat{k}$ displaced the body from a point $(3,4,6)$ to a point $(7,2,5)$ is

Answer 1

Force $\overrightarrow{F}=4\hat{i}+\hat{j}-3\hat{k}$

Displacement $\overrightarrow{d}=(5\hat{i}+4\hat{j}+\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})$

$\overrightarrow{d}=5\hat{i}+4\hat{j}+\hat{k}-\hat{i}-2\hat{j}-3\hat{k}$

$\overrightarrow{d}=4\hat{i}+2\hat{j}-2\hat{k}$

Work $w=\overrightarrow{F}\times \overrightarrow{d}$

$w=(4\hat{i}+\hat{j}-3\hat{k})\cdot (4\hat{i}+2\hat{j}-2\hat{k})$

$w=16\hat{i}+2\hat{j}+6\hat{k}$

$\therefore w=16+2+6$

$w=24$ Unit.