Calculus III vector field

Question

Since I can't write in LaTeX, I will submit an uploaded picture of the questions.

https://ibb.co/5WndnzZ

I'm familiar with the techniques to solve these questions, but unsure how I treat the vector x inside the cross product when finding curl(F), considering F is a vector field of only one variable.

I see F can probably be expressed easier in spherical coordinates, but does that leave me with the vector field F(r, theta, phi) = (1/r³, 0, 0)?

Answer 1

You need to be careful here, x is a vector not the x-component of the vector you can see this when later in the question they gave you x(t) as a vector of three component. So consider F(X) = (x,y,z)/(x^2+y^2+z^2)^2