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Hi, I'm learning vector calc on my own and my book wasn't clear on some basic definitions.

1. My text mentions that a vector function r(t) = <f(t), g(t), h(t)>, where the f(t), g(t), h(t) are real valued functions. What exactly is a real-valued function? Like a function that produces a real number? If that's the case then we can't have a complex vector function?

2. What's the difference between a vector function and a vector field function? In my book all vector functions are of one variable and all vector field functions are of at least 2 variables; is this the difference?

3. What is a scalar field function? It looks exactly like a normal multi or single variable function.

4. How come vectors in a vector field are draw from the input (x,y) coordinate? I thought vectors can be moved so long its direction and magnitude are the same so why not just move all of them to start at the origin? Also, with wind vector fields etc. what rule prevents one from moving the vectors in these fields around which would screw up the analysis?

Thanks.

1. My text mentions that a vector function r(t) = <f(t), g(t), h(t)>, where the f(t), g(t), h(t) are real valued functions. What exactly is a real-valued function? Like a function that produces a real number? If that's the case then we can't have a complex vector function?

2. What's the difference between a vector function and a vector field function? In my book all vector functions are of one variable and all vector field functions are of at least 2 variables; is this the difference?

3. What is a scalar field function? It looks exactly like a normal multi or single variable function.

4. How come vectors in a vector field are draw from the input (x,y) coordinate? I thought vectors can be moved so long its direction and magnitude are the same so why not just move all of them to start at the origin? Also, with wind vector fields etc. what rule prevents one from moving the vectors in these fields around which would screw up the analysis?

Thanks.

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