#### Answer

A vector whose initial point is at the origin is called a position vector.

#### Work Step by Step

The position vector is a vector which starts from $\left( 0,0 \right)$ to a final point. Consider the position vector v,
$\mathbf{v}=a\mathbf{i}+b\mathbf{j}$
It can be rewritten in Cartesian coordinates as $\left( a,b \right)$. This means the horizontal projection is a and vertical projection is b; it can be represented in vector form $\mathbf{v}$ from initial point $\left( 0,0 \right)$ to final point $\left( a,b \right)$. Then, vector $\mathbf{v}$ is called a position vector.
The length or the magnitude of the position vector $\mathbf{v}$ is given by: $\sqrt{{{a}^{2}}+{{b}^{2}}}$.
Therefore, a vector whose initial point is at the origin is called a position vector.