In a three-dimensional Cartesian coordinate system, the position vector \(\mathbf{r}\) of a point \(P(x, y, z)\) can be expressed as:
\[
\mathbf{r} = x \mathbf{i} + y \mathbf{j} + z \mathbf{k}
\]
where \(\mathbf{i}\), \(\mathbf{j}\), and \(\mathbf{k}\) are the
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