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## Main Question or Discussion Point

Hi everybody,

I have one question about vectors of R^3:

First of all, a point is described by its co-ordinates (x,y,z).

A vector r is described in this way:

I hope this makes sense.

Thanks

I have one question about vectors of R^3:

First of all, a point is described by its co-ordinates (x,y,z).

A vector r is described in this way:

**r**=a**x**+b**y**+c**z**,where {**x,y,z**} is the standard basis (the numbers a,b,c are the "coordinates" of the vector). But i have seen in several books that vectors can be written like this:**r**=(x,y,z) where x,y,z are its co-ordinates, as long as the basis is clearly stated. So when we write (x,y,z) we may mean the point, or the vector? For example, if we define a function f:R^3->R^3: (x,y,z)->(f1(x,y,z),f2(x,y,z),f3(x,y,z)) , we can think of f(x,y,z) both as a point and a vector? I mean, can we write**f**(a,b,c)=f1(a,b,c)**x**+f2(a,b,c)**y**+f3(a,b,c)**z**?I hope this makes sense.

Thanks

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