Find curl(curl F) = ∇ × (∇ × F).

Question

F(x, y, z) = 2x^3yzi + yj + 2zk

Answer 1

To find curl(curl F), we first need to calculate curl F:

curl F = (del x F) =
| i j k |
| del/dx del/dy del/dz |
| 2x^3yz y 2z |

= (2z-y)i - 2x^3zj + (3x^2y)k

Now we can calculate ∇ × (curl F):

∇ × (curl F) =
| i j k |
| del/dx del/dy del/dz |
| 2z-y -2x^3z 3x^2y |

= (-6x^2)j - 2yi

Therefore, curl(curl F) = ∇ × (∇ × F) = (-6x^2)j - 2yi.