- #1
Blkmage
- 11
- 0
Homework Statement
http://img818.imageshack.us/f/screenshot20110423at733.png/
http://img856.imageshack.us/f/screenshot20110423at733.png/
If it'll help you guys help me understand this, here are the solutions:
http://img828.imageshack.us/f/screenshot20110423at752.png/
Homework Equations
[tex]\text{curl}\bold{F} = \nabla \times \bold{F}[/tex]
[tex]\text{div}(\bold{F}) = \nabla \cdot \bold{F}[/tex]
The Attempt at a Solution
My problem is that I don't understand what is meant by a "fixed, but arbitrary function" or a "fixed, but arbitrary vector field." Is a fixed function one that is constant? ie [tex]g(x,y,z) = 2[/tex] Is a fixed vector fixed a constant one, like [tex]\bold{F}(x,y,z) = 2\hat{i} + 3\hat{j} - 5\hat{k}[/tex]?
My problem is that I'm not really understanding the nature of these vector operators. I have the solution and it says:
[tex]\text{curl} \nabla g[/tex] is a constant vector whereas
[tex]\text{curl} \bold{F}[/tex] is a vector field
How is it possible that they are not both vector fields. Same with this:
[tex]\text{div} (\text{curl} \bold{F})[/tex] is a constant scalar whereas
[tex]\text{div} (\bold{v} \times \bold{F})[/tex] is a scalar function...
How are these not both scalar functions?