Is the Rotor of This Radius Vector Correct?

[xz5x]

Please help me! I'm not sure if this is a wright place to ask, but...

(vector) F = r^4 r(vector)
Find me rotor of F
Rotor of vector F must be 0, but I don't know how . You can't use this form of radius vector: xi+yj+zk (i, j, k are vectors), just leave r.
Thank you!

 

[Tide]

Use the spherical coordinate form of the curl which you can find here: http://hyperphysics.phy-astr.gsu.edu/hbase/curl.html#c3

 

[xz5x]

Thank you..but I didn't find the wright answer there

 

[Feynman]

What do you need by this question ?
let be must claire

 

[xz5x]

This is what I need:
nabla x F
F = r^4 r (bold are vectors)..(r is radius vector)
The result of this is 0, but I don't know how...
Thank you for your help!

 

[Tide]

Well, if you can't or won't work with spherical coordinates then do it by brute force using the definition of curl. Just remember that the unit vector \hat r is not a constant with respect to position!

 

[xz5x]

Tide, I really don't know what to do with spherical coordinates. Maybe you can show me.
But, I found another way..Here it is:

nabla x r^4r =
= r^4rotr - r x grad r^4
= 0 - r x dr^4/dr r/r
= - r x dr^4/dr r/r
= - dr^4/dr 1/r rxr
= 0

btw. bold are vectors; curl=rot; nablaxnablaf=0; rot r=0; rxr=0

Can somebody tell me is this correct?