Any point in the universe can be located with a \(3 \times 1\) vector known as the position vector represented as:
\[P = \begin{bmatrix}x \\ y \\ z\end{bmatrix}\]Given a position vector we can say which coordinate system the vector belongs to by writing the vector as \(^{A}P\). Here the vector \(P\) belongs to the coordinate system \(A\).
ach component of vector \(^AP\) tells us the distances along the axes of the coordinate system it belongs to.