find the third vertex of triangle whose centroid is origin and two vertices are (2,4,6) and (0,-2,5)

Explanation

To find the third vertex of a triangle given that the centroid is at the origin and two vertices are (2, 4, 6) and (0, -2, 5), we can follow these steps:

### Step 1: Understand the formula for the centroid
The centroid (G) of a triangle with vertices A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3) is given by the formula:
\[ G = \left( \frac{x1 + x2 + x3}{3}, \frac{y1 + y2 + y3}{3}, \frac{z1 + z2 + z3}{3} \right) \]
In this case, we know that the centroid is at the origin (0, 0, 0).
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