Vector field and Line Integrals

Dear teacher, I have a problem:

How is r parametrized in the task below? This is needed for finding W, which is given by:

W = ∫c F • dr.

7. Find the work done by the force field

F = (x + y)i + (x - z)j + (z - y)k

in moving an object from (1,0,-1) to (0,-2,3) along any smooth curve.

Best regards

Re: Vector field and Line Integrals

Quote:

Originally Posted by

**kaemper** Dear teacher, I have a problem:

How is r parametrized in the task below? This is needed for finding W, which is given by:

W = ∫c F • dr.

7. Find the work done by the force field

F = (x + y)i + (x - z)j + (z - y)k

in moving an object from (1,0,-1) to (0,-2,3) along any smooth curve.

Best regards

Take the Curl of your vector field. What does that value suggest exists? Find this and you don't need to worry about the actual path for your integral.