The plane `2x+3y+4z=12` meets the coordinate axes in A,B and C. The centroid of `triangleABC` is

Options

A. `(2,3,4)
B. (6,4,3)
C. `(2,4/3,1)`
D. none of these

Answer

c

Explanation

The given equation `x/6+y/4+c/3=1`.
This plane meets the coordinate axes in A(6,0,0), B(0,4,0) and C(0,0,3).
`therefore` centroid of `triangleABC` is `G((6+0+0)/3, (0+4+0)/3,(0+0+3)/3)` i.e., `G(2,4/3,1)`.