TransformedField["Cartesian"->"Spherical",{0,0,1} ,{x,y,z}->{r,\[Theta],\[CurlyPhi]}]//Simplify//MatrixForm
This gives the correct transformed vector in Spherical: {Cos[\[Theta]], -Sin[\[Theta]],0}, which is dependent on the starting point of the vector. If I make it start from the origin, i.e.,\[Theta] ->0, it becomes the same as transforming point {0,0,1} into Spherical, which is {1,0,0}. Everything is good.
However, if I want to transform a general vector, say {x,y,z}.
TransformedField["Cartesian"->"Spherical",{x,y,z} ,{x,y,z}->{r,\[Theta],\[CurlyPhi]}]//Simplify//MatrixForm
It goes directly to {r,0,0}, which means TransformedField treats {x,y,z} as a position vector rather than a general. It seems the behavior of TransformedField depends on the input: {0,0,1} or {x,y,z}. Do I get it right?
I was wondering how I would transform a symbolic vector without it being treated as a position vector.
Thank you!