how do I make difference between vector valued functions and vector fields, I am confused how they differ and how are they same? Which is used with what?(adsbygoogle = window.adsbygoogle || []).push({});

What about a function F(x,y,z,t) = (f1(x,y,z,t), f2(x,y,z,t), f3(x,y,z,t)) which maps R4 to R3, what type of function is this?

F(x,y) = x^2 + 2y

F(x,y,z) = x^2 + y^2 + 10z

F(x,y,z,t) = 3x + 2y - z^2 + t

F(t) = (t^2 , 0 , t^3)

F(x,y) = (x^2 + y, y^2 - x)

F(x,y,z) = (z+xy,y^2+z, 2x-z)

F(x,y,z,t) = (z-t^2,y^2, xt+z)

which of these functions is what type and why? Also what is a potential field. Finally how do they all (vector field, potential field, vector valued function) differ when compared to curve/surface in R3?

A short description shall suffice, thanks. Its just that I can't find the answer summarised anywhere making good distinction.

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# About Vector fields and vector valued functions

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