Concept:Centroid: The point at which the three medians of the triangle intersect is known as the centroid of a triangle.If the three vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3), then the \(\displaystyle G(x,y)=\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)\)Calculation:Given:A, B, and C are vertices of the trianglePosition vectors of A, B, and C be \(\displaystyle ? a,\ ? b,\ ? c\)G is the centroid of = ?ABC? G = \(\displaystyle \frac{\vec a + \vec b + \vec c}{3} \)? \(\overrightarrow{AG}\) = \(\displaystyle \frac{(\vec a+\vec b+\vec c)}{3} - \vec{a}\)? \(\overrightarrow{AG}\) = \(\displaystyle \frac{(a+\vec b+\vec c)-3\vec{a}}{3}\)?\(\overrightarrow{AG}\) = \(\displaystyle\frac{\vec b + \vec c -2\vec a}{3}\)?? \(\overrightarrow{AG}\) = \(\displaystyle\frac{\vec b + \vec c -2\vec a}{3}\)