The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3,-5,7) and (-1,7,-6) respectively, find the coordinates of the point C.

Explanation

To find the coordinates of point C in triangle ABC given the centroid G and the coordinates of points A and B, we can follow these steps:

### Step 1: Understand the Centroid Formula
The centroid (G) of a triangle with vertices A, B, and C is given by the formula:
\[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}, \frac{z_1 + z_2 + z_3}{3} \right) \]
where \(A(x_1, y_1, z_1)\), \(B(x_2, y_2, z_2)\), and \(C(x_3, y_3, z_3)\).
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