## Position Vector

In physics, the position, the **position vector** or the **location vector** of a body *with respect to a coordinate system* is defined as the vector that links the location of the body with the origin of the coordinate system. In *Cartesian coordinates*, it is expressed as:

Where:

- $\overrightarrow{r}$ : Is the
**position vector** *x*,*y,**z*: Are the**coordinates**of the position vector- $\overrightarrow{i}\text{,}\overrightarrow{j}\text{,}\overrightarrow{k}$ : Are the
**unit vectors**in the directions of axes OX, OY and OZ respectively.

The **unit of measurement** for position in the International System is meter [m]. Like all vectors, the position vector in physics has direction and magnitude (also known as size, modulus or length of the vector). The magnitude of the position vector is the distance of the body to the origin of the reference system. To calculate it you can use the following formula:

For those problems where you are working in fewer dimensions, you can simplify the previous formula by eliminating unnecessary terms. This way, the position equation:

- In two dimensions becomes $\overrightarrow{r}=x\overrightarrow{i}+y\overrightarrow{j}+\overline{)z\overrightarrow{k}}=x\overrightarrow{i}+y\overrightarrow{j}$ ,and its magnitude $\left|\overrightarrow{r}\right|=\sqrt{{x}^{2}+{y}^{2}+\overline{){z}^{2}}}=\sqrt{{x}^{2}+{y}^{2}}$, since
*z=0* - In one dimension becomes $\overrightarrow{r}=x\overrightarrow{i}+\overline{)y\overrightarrow{j}}+\overline{)z\overrightarrow{k}}=x\overrightarrow{i}$, and its magnitude $\left|\overrightarrow{r}\right|=\sqrt{{x}^{2}+\overline{){y}^{2}}+\overline{){z}^{2}}}=\sqrt{{x}^{2}}=x$, since
*y=0*and*z=0*

We have represented a position vector in three dimensions (left) and another in two dimensions (right) in the following figure: