Question

A particle acted on by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ is displaced from the point $(1,2,3)$ to $(5,4,1)$ the work done is

• A. $20$
• B. $30$
• C. $40$
• D. $50$

Answer 1

The correct option is C $40$

Displacement vector is $\overrightarrow{s}=5\hat{i}+4\hat{j}+\hat{k}-(\hat{i}+2\hat{j}+3\hat{k})$
$=4\hat{i}+2\hat{j}-2\hat{k}$
$\overrightarrow{F}=$Force vector$=4\hat{i}+\hat{j}-3\hat{k}+3\hat{i}+\hat{j}-\hat{k}$
$=7\hat{i}+2\hat{j}-4\hat{k}$
work done$=\overrightarrow{F}.\overrightarrow{S}$
$=(7\hat{i}+2\hat{j}-4\hat{k}).(4\hat{i}+2\hat{j}-2\hat{k})$
$=28+4+8=40$