A plane cuts the co-ordinate axes at A, B and C respectively. If the centroid of `DeltaABC` is `(2,-3,4)`, find the equation of the plane.

Explanation

To find the equation of the plane that cuts the coordinate axes at points A, B, and C, given that the centroid of triangle ABC is (2, -3, 4), we can follow these steps:

### Step 1: Set up the equation of the plane
The general equation of a plane that intersects the coordinate axes at points A, B, and C can be written as:
\[ \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 \]
where \(a\), \(b\), and \(c\) are the x-intercept, y-intercept, and z-intercept of the plane, respectively.
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