Chapter 16.1 Review

Question 1

What is a vector field in three dimensions represented by and what does a vector field even do?

Answer 1

A vector field assiagns a vector each point in the a domain and it is represnted by a triple function called F=

Question 2

What is a vector field in two dimension represented by?

Answer 2

A vector field in two dimension is represented by a pair of functions: F=<f1></f1>

Question 3

What happens if F=∇V?

What does this also imply?

Answer 3

Then V is called a potentional Function for F.

This must also imply that some differentialilty component involved for F.

Question 4

What is F called if it has a potential function?

Answer 4

F is called conseravtive if it has a potential function.

Question 5

How do any two potential functions for a conseravtice vector field differ?

Answer 5

On an open, connected domain, the potential functions will differ by a constant.

Question 6

write the expression for the conservaticee vector fields F that satisfies the cross-partial condiction.

Answer 6

(that image is on my email, please check it out)

dF1/dy=dF2/dx, dF1/dz=dF3/dx, dF2/dz=dF3/dy