Line integral

1. Jan 24, 2006

zekester

i have a force field F = 2xy*(ux)+(x^2-z^2)(uy)-3xz^2(uz) where ux,uy,and uz are unit vectors in the direction indicated. I have to find the work done by the field on a particle that travels from A(0,0,0) to
B(2,1,3) on a straight line. work is regarded as the integral from A to B of the dot product of F and dl = dx(ux)+dy(uy)+dz(uz). I'm not quite sure how to do this.

2. Jan 24, 2006

siddharth

You can introduce a common vairable of integration to solve this.
Since
$$\int_{A}^{B} \vec{F}.d\vec{r} = \int_{t1}^{t2} \vec{F}.(\vec{\frac{dr}{dt}}) dt$$

Where $$\vec{r}$$ (and F) can be expressed as a function of t.

Last edited: Jan 24, 2006
3. Jan 24, 2006

ok, thanks