Question

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

• A. $15\text{units}$
• B. $25\text{units}$
• C. $20\text{units}$
• D. $10\text{units}$

Answer 1

The correct option is A $15\text{units}$

$\overrightarrow{F}=3\hat{i}+9\hat{j}+5\hat{k}$

displacement vector $\overrightarrow{b}=(7-3)\hat{i}+(2-4)\hat{j}+(5-6)\hat{k}$

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

so work $W=\overrightarrow{F}.\overrightarrow{d}=3\left(4\right)+(-4)(-2)+5(-1)$

or $W=12+8-5=15unit$