Line integrals and vector fields.

[spyroarcher]

Homework Statement

There is a circle of equation x^2+y^2=1 and a vector field F (x; y) =< y + .5x, x + .3y >.
Imagine the field zoomed in extremely close at (0,1), to the point where it looks like a constant field of <-1,.3>. Calculate the work from say (0,1) to (-.001, 1). The constant field is force.

Homework Equations

I was told to do this I dot <-1,3> and the vector made by (0,1) to (-.001,1).

The Attempt at a Solution

I receive an extremely tiny negative number, and I think it is wrong because when going right to left, the value looks like it should be positive. I think I somehow got the vector made by the 2 points wrong, cause I get <1,1.001>.

Thanks in advance.

 

[LCKurtz]

Homework Statement

There is a circle of equation x^2+y^2=1 and a vector field F (x; y) =< y + .5x, x + .3y >.
Imagine the field zoomed in extremely close at (0,1), to the point where it looks like a constant field of <-1,.3>. Calculate the work from say (0,1) to (-.001, 1). The constant field is force.

Homework Equations

I was told to do this I dot <-1,3> and the vector made by (0,1) to (-.001,1).

The Attempt at a Solution

I receive an extremely tiny negative number, and I think it is wrong because when going right to left, the value looks like it should be positive. I think I somehow got the vector made by the 2 points wrong, cause I get <1,1.001>.

Thanks in advance.

The vector from your start point to the second point is D = <-.001,1> - <0,1> = <-.001,0>. Dotting that into your force will yield a positive number.