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The centroid of a triangle ABC is at th...

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.

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To find the coordinates of point C in triangle ABC, we can use the formula for the centroid of a triangle in three-dimensional space. 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: - \( (x_1, y_1, z_1) \) are the coordinates of point A, ...
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