\( \vec { X M } = \frac { 1 } { 3 } ( \vec { X A } + \vec { X B } + \vec { X C } ) \)

The equation you've provided appears to represent a vector relationship in a geometric context, possibly involving points \( A \), \( B \), \( C \), and \( M \) in a coordinate system. The expression \( \vec{XM} = \frac{1}{3} (\vec{XA} + \vec{XB} + \vec{XC}) \) suggests that the vector \( \vec{XM} \) is the average of the vectors \( \vec{XA} \), \( \vec{XB} \), and \( \vec{XC} \). This can be interpreted as follows: 1. **Vectors**: - \( \vec{XA} \) is the vector from point \( X \) to point \( A \). - \( \vec{XB} \) is the vector from point \( X \) to point \( B \). - \( \vec{XC} \) is the vector from point \( X \) to point \( C \). - \( \vec{XM} \) is the vector from point \( X \) to point \( M \). 2. **Interpretation**: - The equation indicates that point \( M \) is located at the centroid of the triangle formed by points \( A \), \( B \), and \( C \) when viewed from point \( X \). In other words, \( M \) is the point that is equidistant from the average positions of points \( A \), \( B \), and \( C \) relative to point \( X \). 3. **Geometric Context**: - If \( A \), \( B \), and \( C \) are vertices of a triangle, then \( M \) can be interpreted as the centroid of that triangle, which is the point where the three medians intersect. The centroid divides each median into a ratio of 2:1. If you have a specific question or need further clarification on this equation, please let me know!