Consider these two expressions
\(X(x_1,\dots ,x_n)\) and \(\Vect{x} = (x_1,\dots ,x_n)\).
In the first expression the \(n\)-tuple \((x_1,\dots ,x_n)\) characterizes the location of a point. In the second expression the same \(n\)-tuple forms a vector. This ambiguity in notation is firmly entrenched in the literature. Fortunately, we can untangle it nicely if we keep in mind the following dictionary for translating between points and vectors.
\[ \xymatrix@C=15pt{ *+[F-,]{ \begin{array}{c} \text{A given point} \\ X(x_1,\dots ,x_n) \end{array} } \ar[rr] & & *+[F-,]{ \begin{array}{c} \text{yields the vector}\ \Vect{x}=(x_1,\dots ,x_n). \\ \text{It is represented by the arrow}\ \Arrow{\Vect{0}}{X}. \\ \text{We call}\ \Vect{x}\ \text{the position vector of $X$.} \end{array} } \\ % *+[F-,]{ \begin{array}{c} \text{A given vector} \\ \Vect{x}=(x_1,\dots ,x_n) \end{array} } \ar[rr] & & *+[F-,]{ \begin{array}{c} \text{yields the point}\ X(x_1,\dots ,x_n).\\ \text{It is the tip of the arrow with tail at}\ \Vect{0} \\ \text{and representing}\ \Vect{x}. \end{array} } } \]