Find the curl at (1,-1,2)

Question

https://i.imgur.com/OaByXwq.png

 

Answer 1

A=<3xz²,-yz,x+2z>. Let A₁=3xz², A₂=-yz, A₃=x+2z.

Curl uses the grad operator ∇=<∂/∂x,∂/∂y,∂/∂z> and the vector product:

∇᰽A=<∂A₃/∂y-∂A₂/∂z,-∂A₃/∂x+∂A₁/∂z,∂A₂/∂x-∂A₁/∂y>=<y,6xz-1,0>.

Let A₁=y, A₂=6xz-1, A₃=0.

Curl(∇᰽A)=<-6x,0,6z-1>.

Now we plug in (1,-1,2):

Curl(curl(A))=<-6,0,11>.

Magnitude |Curl(curl(A))|=√(6²+0²+11²)=√157=12.53.