Answer to Question #98591 in Analytic Geometry for Emmanuel

Question

The work done in moving an object along a straight line from (3, 2, -1) to (2, -1, 4) in a force field by F=4i-3j+2k\n

Answer 1

The general equation for the work done in a force field is as follows: $\int_a^b \overrightarrow{F}(\overrightarrow{r}(t))\cdot \overrightarrow{r}'(t)dt$ .

However, since an object is moving in a straight line and the force is constant, is it can be written just as $\overrightarrow{F}\cdot\overrightarrow{\Delta r}$ .

We then compute $\overrightarrow{F} = (4, -3, 2)$ and $\overrightarrow{\Delta r} = (2, -1, 4) - (3, 2, -1) = (-1, -3, 5)$.

Finally, work done is

$\overrightarrow{F}\cdot\overrightarrow{\Delta r} = (4, -3, 2) \cdot (-1, -3, 5) = -4 + 9 + 10 =$ 15.

Answer: 15.