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 \( c \) given that the origin is the centroid of the triangle \( PQR \) with vertices \( P(2a, 2, 6) \), \( Q(4, 3b, 10) \), and \( R(8, 14, 2c) \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Centroid Formula**:
The centroid \( G \) of a triangle with vertices \( P(x_1, y_1, z_1) \), \( Q(x_2, y_2, z_2) \), and \( R(x_3, y_3, z_3) \) is 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)
...