If the origin is the centroid of the triangle PQR with vertices `P (2a , 2, 6)`, `Q ( 4, 3b , 10)`and `R(8, 14 , 2c)`, then find the values of a, b and c.

Explanation

To find the values of \(a\), \(b\), and \(c\) such that the origin is the centroid of the triangle with vertices \(P(2a, 2, 6)\), \(Q(4, 3b, 10)\), and \(R(8, 14, 2c)\), we will use the formula for the centroid of a triangle in three-dimensional space.

### Step 1: Write the formula for the centroid
The coordinates of the centroid \(G\) of a triangle with vertices \(P(x_1, y_1, z_1)\), \(Q(x_2, y_2, z_2)\), and \(R(x_3, y_3, z_3)\) are given by:
\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}, \frac{z_1 + z_2 + z_3}{3}\right) \]

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