If ` vec a ,\ vec b ,\ vec c` are position vectors of the vertices of a triangle, then write the position vector of its centroid.

Explanation

To find the position vector of the centroid of a triangle with vertices represented by the position vectors \( \vec{a}, \vec{b}, \vec{c} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Centroid**:
The centroid of a triangle is the point where the three medians intersect. It divides each median in a 2:1 ratio.

2. **Identify the Vertices**:
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