Question

If a force \(\vec{F}=\hat{i}-2\hat{j}-4\hat{k}\) acting on a particle displaces it from \((1,1,1)\) to \((2,-1,0)\), then the work done by the force (in units of work) is

• A. \(7\)
• B. \(1\)
• C. \(5\)
• D. \(4\)
• E. \(9\)

Hint:

For work done by a constant force in 3D: \[ W=\vec{F}\cdot \Delta \vec{r} \] Always compute displacement first.

Answer 1

The Correct Option is A

Displacement: \[ \Delta \vec{r}=(2-1)\hat{i}+(-1-1)\hat{j}+(0-1)\hat{k} =\hat{i}-2\hat{j}-\hat{k} \] Work done: \[ W=\vec{F}\cdot \Delta \vec{r} \] \[ =(\hat{i}-2\hat{j}-4\hat{k})\cdot(\hat{i}-2\hat{j}-\hat{k}) \] \[ =1+4+4=9 \] So the direct calculation gives: \[ \boxed{9} \] which corresponds to option (E), not (A).