Question

the work done by a force f=3i-4j+5k displaces the body from a point (3,4,6) to a point (7,2,5) is

Answer 1

Given, $\vec{F}=3\hat{i}-4\aht{j}+5\hat{k}$
body displaces from a point (3,4,6) to a point (7,2,5) .
so, displacement vector, $\vec{r}=(7-3)\hat{i}+(2-4)\hat{j}+(5-6)\hat{k}$
or, $\vec{r}=4\hat{i}-2\hat{j}-\hat{k}$

we know, workdone is the dot product of force and displacement along force.

e.g., $W=\vec{F}.\vec{r}$

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

= 3 × 4 - 4 × -2 + 5 × -1

= 12 + 8 - 5 = 15 J

hence, workdone = 15J

Answer 2

Explanation:

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