Question

How do I show that F is conservative if F is a plane vector field that has the same value at every point?

Answer 1

are there options to this?

Answer 2

nope

Answer 3

Is something like this helpful?

http://tutorial.math.lamar.edu/Classes/CalcIII/ConservativeVectorField.aspx

Answer 4

I've been looking at that too, but I'm just not sure how to do the "same value at every point" part...

Answer 5

if some vector field has the same value at every point, then the vectors in the field are independent of the xy position; i.e. they are constant

Answer 6

so this vector field can be written\[\vec F(x,y)=a\hat i+b\hat j\]

Answer 7

should be straight forward from here....

Answer 8

thanks!