If $\vec r=x\hat i+y\hat j+z\hat k$ where $r=|\hat r|$ , and $\vec a$ is a constant vector then find the values of following
1) $\nabla\times(r^n\ \vec r)$
2) $\nabla\times(\vec a\times \vec r)$
My trial:
1) $\ \nabla\times(r^n\ \vec r)=r^n(\nabla\times \vec r)=r^n(0)=0$
2) $\nabla\times(\vec a\times \vec r)=(\nabla\cdot\vec r)\vec a-(\nabla\cdot\vec a)\vec r=3\vec a-0=3\vec a$
I don't know if i have done any mistake or my answers are incorrect. please help me solve these problems. thanks