**1. Homework Statement**

Let

**r**be a position vector from the origin (

**r**=x

**i**+y

**j**+z

**k**), whose magnitude is r, and let f(r) be a scalar function of

**r**. Sketch the field lines of f(r)

**r**

**2. Homework Equations**

1 [tex]\nabla[/tex]x([tex]\nabla[/tex][tex]\Psi[/tex])=0

2 [tex]\nabla[/tex].([tex]\nabla[/tex]x

3 [tex]\nabla[/tex]x([tex]\nabla[/tex]x

4 [tex]\nabla[/tex].([tex]\Psi[/tex]

5 [tex]\nabla[/tex]x([tex]\Psi[/tex]

6 [tex]\nabla[/tex].(

7 [tex]\nabla[/tex]x(

I can't get started on this question. I have no idea how you can draw a sketch of the field lines when the scalar function is unknown. My intuition says you should be able to use some of those identities but I need a push in the right direction. Please, someone give me that.

1 [tex]\nabla[/tex]x([tex]\nabla[/tex][tex]\Psi[/tex])=0

2 [tex]\nabla[/tex].([tex]\nabla[/tex]x

**v**)=03 [tex]\nabla[/tex]x([tex]\nabla[/tex]x

**v**)=[tex]\nabla[/tex]([tex]\nabla[/tex].**v**)-[tex]\nabla[/tex][tex]^{}2[/tex]**v**4 [tex]\nabla[/tex].([tex]\Psi[/tex]

**v**)=[tex]\Psi[/tex][tex]\nabla[/tex].**v**+**v**.[tex]\nabla[/tex][tex]\Psi[/tex]5 [tex]\nabla[/tex]x([tex]\Psi[/tex]

**v**)=[tex]\Psi[/tex][tex]\nabla[/tex]x**v**+([tex]\nabla[/tex][tex]\Psi[/tex])x**v**6 [tex]\nabla[/tex].(

**v.w**=**w.**([tex]\nabla[/tex]x**v**)-**v**.([tex]\nabla[/tex]x**w**)7 [tex]\nabla[/tex]x(

**vxw**=**v**([tex]\nabla[/tex].**w**-**w**([tex]\nabla[/tex].**v**+(**w**.[tex]\nabla[/tex])**v**-(**v**.[tex]\nabla[/tex])**w****3. The Attempt at a Solution**I can't get started on this question. I have no idea how you can draw a sketch of the field lines when the scalar function is unknown. My intuition says you should be able to use some of those identities but I need a push in the right direction. Please, someone give me that.