Question

A force $\vec{F} = \left(5\hat{i}+3\hat{j}+2\hat{k}\right)N$ is applied over a particle which displaces it from its origin to the poin $\vec{r} = \left(2\hat{i} − \hat{j}\right)m.$ The work done on the particle in joules is

• A. −7
• B. +7
• C. +10
• D. +13

Answer 1

Answer: (B)

Work done, $W = \vec{F}\cdot\vec{s}$
Here $\vec{s} = \vec{r_{f}} - \vec{r_{i}} = \left(2\hat{i}-\hat{j}\right)$
$W = \left(5\hat{i}+3\hat{j}+2\hat{k}\right) \left(2\hat{i}-\hat{j}\right) = 10-3 = 7\,J.$