# Calc 2 vectors

1. Apr 25, 2010

### somebodyelse5

1. The problem statement, all variables and given/known data

A constant force F=4i+2j+2k moves an object along a straight line from the point (1, -5, 1) to the point (1, -1, 0).

Find the work done if the force is measured in newtons and the position is measured in meters.

2. Relevant equations

W=Fd

3. The attempt at a solution

I used the distance formula to find the distance between the two points which is sqrt(17)

But what is the correct way to multiply the Force vector by this distance?

2. Apr 25, 2010

### Phrak

1. Add up the x y and z components of work or 2. use the dot product of F and D, where D is the displacement.

3. Apr 25, 2010

### gabbagabbahey

You should get in the habit of using the more general definition of work from $\textbf{r}_1$ to $\textbf{r}_2$:

$$W=\int_{\textbf{r}_1}^{\textbf{r}_2} \textbf{F}\cdot d\textbf{r}$$

In your case, $\textbf{F}$ is uniform so you can pull it out of the integral

$$W=\textbf{F}\cdot\int_{\textbf{r}_1}^{\textbf{r}_2}d\textbf{r}=\textbf{F}\cdot(\textbf{r}_2-\textbf{r}_1)$$