A plane meets the coordinate axes in `A ,B ,C` such that eh centroid of triangle `A B C` is the point `(p ,q ,r)dot` Show that the equation of the plane is `x/p+y/q+z/r=3.`

Explanation

To solve the problem, we need to show that the equation of the plane that meets the coordinate axes at points A, B, and C, where the centroid of triangle ABC is the point (p, q, r), is given by the equation \( \frac{x}{p} + \frac{y}{q} + \frac{z}{r} = 3 \).

### Step-by-Step Solution:

1. **Identify Points A, B, and C**:
- The plane intersects the x-axis at point A, which can be represented as \( A(x_1, 0, 0) \).
- The plane intersects the y-axis at point B, represented as \( B(0, y_1, 0) \).
- The plane intersects the z-axis at point C, represented as \( C(0, 0, z_1) \).
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