Direction of position vectors

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I've been trying to learn Barycentric coordinates and came across the following definition:

enter image description here

I am confused if $\vec A, \vec B, \vec C$ are denoted as $\vec {PA}, \vec {PB}, \vec {PC}$ respectively or it denotes $\vec {OA}, \vec {OB}, \vec {OC}$ where $O$ is the origin different from any of the points mentioned.

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here is a sketch of the definition

A,B,C and P are points on the plane

$\vec{A},\vec{B},\vec{C}$ and $\vec{P}$ are the corresponding vectors from the origin

enter image description here