Question:If $\vec F$ is a solenoidal field, then curl curl curl $\vec F$=
a)$\nabla^4\vec F$
b)$\nabla^3\vec F$
c)$\nabla^2\vec F$
d) none of these.
My approach:I first calculate $\nabla×\nabla×\vec F$. We know that $$\nabla\times\left(\nabla\times\textbf{F}\right)=\nabla\left(\nabla\cdot\textbf{F}\right)-\nabla^2\textbf{F}$$ and since $\vec F$ is solenoidal,$\nabla\cdot\textbf{F}=0$,there fore we have $$\nabla\times\left(\nabla\times\textbf{F}\right)=-\nabla^2\textbf{F}$$ Now for $\nabla×\nabla×\nabla×\vec F$ I am unable to proceed,and totally stuck how to proceed further!I guess the answer is (b) but I have no idea.
Please guide me with correct answer!
Thanks in advance.