Vector Algebra

Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be the position vectors of the vertices of a \(\triangle A B C\). Through the vertices, lines are drawn parallel to the sides to form the \(\Delta A^{\prime} B^{\prime} C^{\prime}\). Then, the centroid of \(\Delta A^{\prime} B^{\prime} C^{\prime}\) is